prompt listlengths 1 27 | label stringlengths 1 23 | metadata dict |
|---|---|---|
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{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设 a_n=\\left(\\df{1+q}{1-q}\\right)\\cdot\\left(\\df{1+q^2}{1-q^2}\\right)^{\\frac{1}{2}}\\cdot\\left(\\df... | 42 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设 a_n=\\left(\\df{1+q}{1-q}\\right)\\cdot\\left(\\df{1+q^2}{1-q^2}\\right)^{\\frac{1}{2}}\\cdot\\left(\\df... | 42 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设 a_n=\\left(\\df{1+q}{1-q}\\right)\\cdot\\left(\\df{1+q^2}{1-q^2}\\right)^{\\frac{1}{2}}\\cdot\\left(\\df... | 42 | {
"assistant_turn_index": 0,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设 a_n=\\left(\\df{1+q}{1-q}\\right)\\cdot\\left(\\df{1+q^2}{1-q^2}\\right)^{\\frac{1}{2}}\\cdot\\left(\\df... | 42 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设 a_n=\\left(\\df{1+q}{1-q}\\right)\\cdot\\left(\\df{1+q^2}{1-q^2}\\right)^{\\frac{1}{2}}\\cdot\\left(\\df... | 42 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设 a_n=\\left(\\df{1+q}{1-q}\\right)\\cdot\\left(\\df{1+q^2}{1-q^2}\\right)^{\\frac{1}{2}}\\cdot\\left(\\df... | 42 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数 $f(x)=\\frac{x^{2}+x+16}{x}(2 \\leq x \\leq a)$, 其中实数 $a>2$. 若 $f(x)$ 的值域为 $[9,11]$, 则 $a$ 的取值范围是一个区间$... | 12 | {
"assistant_turn_index": 1,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数 $f(x)=\\frac{x^{2}+x+16}{x}(2 \\leq x \\leq a)$, 其中实数 $a>2$. 若 $f(x)$ 的值域为 $[9,11]$, 则 $a$ 的取值范围是一个区间$... | 12 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数 $f(x)=\\frac{x^{2}+x+16}{x}(2 \\leq x \\leq a)$, 其中实数 $a>2$. 若 $f(x)$ 的值域为 $[9,11]$, 则 $a$ 的取值范围是一个区间$... | 12 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数 $f(x)=\\frac{x^{2}+x+16}{x}(2 \\leq x \\leq a)$, 其中实数 $a>2$. 若 $f(x)$ 的值域为 $[9,11]$, 则 $a$ 的取值范围是一个区间$... | 12 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数 $f(x)=\\frac{x^{2}+x+16}{x}(2 \\leq x \\leq a)$, 其中实数 $a>2$. 若 $f(x)$ 的值域为 $[9,11]$, 则 $a$ 的取值范围是一个区间$... | 12 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数 $f(x)=\\frac{x^{2}+x+16}{x}(2 \\leq x \\leq a)$, 其中实数 $a>2$. 若 $f(x)$ 的值域为 $[9,11]$, 则 $a$ 的取值范围是一个区间$... | 12 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数 $f(x)=\\frac{x^{2}+x+16}{x}(2 \\leq x \\leq a)$, 其中实数 $a>2$. 若 $f(x)$ 的值域为 $[9,11]$, 则 $a$ 的取值范围是一个区间$... | 12 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数 $f(x)=\\frac{x^{2}+x+16}{x}(2 \\leq x \\leq a)$, 其中实数 $a>2$. 若 $f(x)$ 的值域为 $[9,11]$, 则 $a$ 的取值范围是一个区间$... | 12 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the perimeter of the right triangle whose exradius of the hypotenuse is $30$?\n\nRemember to put y... | 60 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the perimeter of the right triangle whose exradius of the hypotenuse is $30$?\n\nRemember to put y... | 60 | {
"assistant_turn_index": 0,
"total_assistant_turns": 1
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the perimeter of the right triangle whose exradius of the hypotenuse is $30$?\n\nRemember to put y... | 60 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the perimeter of the right triangle whose exradius of the hypotenuse is $30$?\n\nRemember to put y... | 60 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the perimeter of the right triangle whose exradius of the hypotenuse is $30$?\n\nRemember to put y... | 60 | {
"assistant_turn_index": 2,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the perimeter of the right triangle whose exradius of the hypotenuse is $30$?\n\nRemember to put y... | 60 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the perimeter of the right triangle whose exradius of the hypotenuse is $30$?\n\nRemember to put y... | 60 | {
"assistant_turn_index": 2,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the perimeter of the right triangle whose exradius of the hypotenuse is $30$?\n\nRemember to put y... | 60 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the perimeter of the right triangle whose exradius of the hypotenuse is $30$?\n\nRemember to put y... | 60 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the perimeter of the right triangle whose exradius of the hypotenuse is $30$?\n\nRemember to put y... | 60 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn the figure, $ABCD$ is a $2 \\times 2$ square, $E$ is the midpoint of $\\overline{AD}$, and $F$ is on $\... | 16 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn the figure, $ABCD$ is a $2 \\times 2$ square, $E$ is the midpoint of $\\overline{AD}$, and $F$ is on $\... | 16 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn the figure, $ABCD$ is a $2 \\times 2$ square, $E$ is the midpoint of $\\overline{AD}$, and $F$ is on $\... | 16 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn the figure, $ABCD$ is a $2 \\times 2$ square, $E$ is the midpoint of $\\overline{AD}$, and $F$ is on $\... | 16 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn the figure, $ABCD$ is a $2 \\times 2$ square, $E$ is the midpoint of $\\overline{AD}$, and $F$ is on $\... | 16 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn the figure, $ABCD$ is a $2 \\times 2$ square, $E$ is the midpoint of $\\overline{AD}$, and $F$ is on $\... | 16 | {
"assistant_turn_index": 1,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn the figure, $ABCD$ is a $2 \\times 2$ square, $E$ is the midpoint of $\\overline{AD}$, and $F$ is on $\... | 16 | {
"assistant_turn_index": 0,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn the figure, $ABCD$ is a $2 \\times 2$ square, $E$ is the midpoint of $\\overline{AD}$, and $F$ is on $\... | 16 | {
"assistant_turn_index": 0,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn the figure, $ABCD$ is a $2 \\times 2$ square, $E$ is the midpoint of $\\overline{AD}$, and $F$ is on $\... | 16 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn the figure, $ABCD$ is a $2 \\times 2$ square, $E$ is the midpoint of $\\overline{AD}$, and $F$ is on $\... | 16 | {
"assistant_turn_index": 0,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nCircles of radius $2$ and $3$ are externally tangent and are circumscribed by a third circle, as shown in ... | 12 | {
"assistant_turn_index": 0,
"total_assistant_turns": 1
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nCircles of radius $2$ and $3$ are externally tangent and are circumscribed by a third circle, as shown in ... | 12 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nCircles of radius $2$ and $3$ are externally tangent and are circumscribed by a third circle, as shown in ... | 12 | {
"assistant_turn_index": 2,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nCircles of radius $2$ and $3$ are externally tangent and are circumscribed by a third circle, as shown in ... | 12 | {
"assistant_turn_index": 0,
"total_assistant_turns": 7
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nCircles of radius $2$ and $3$ are externally tangent and are circumscribed by a third circle, as shown in ... | 12 | {
"assistant_turn_index": 1,
"total_assistant_turns": 7
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nCircles of radius $2$ and $3$ are externally tangent and are circumscribed by a third circle, as shown in ... | 12 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nCircles of radius $2$ and $3$ are externally tangent and are circumscribed by a third circle, as shown in ... | 12 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nCircles of radius $2$ and $3$ are externally tangent and are circumscribed by a third circle, as shown in ... | 12 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the coefficient of $x^3$ when $7x^4-3x^3 -3x^2-8x + 1$ is multiplied by $8x^4+2x^3 - 7x^2 + 3x + 4... | 37 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the coefficient of $x^3$ when $7x^4-3x^3 -3x^2-8x + 1$ is multiplied by $8x^4+2x^3 - 7x^2 + 3x + 4... | 37 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the coefficient of $x^3$ when $7x^4-3x^3 -3x^2-8x + 1$ is multiplied by $8x^4+2x^3 - 7x^2 + 3x + 4... | 37 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the coefficient of $x^3$ when $7x^4-3x^3 -3x^2-8x + 1$ is multiplied by $8x^4+2x^3 - 7x^2 + 3x + 4... | 37 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the coefficient of $x^3$ when $7x^4-3x^3 -3x^2-8x + 1$ is multiplied by $8x^4+2x^3 - 7x^2 + 3x + 4... | 37 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the coefficient of $x^3$ when $7x^4-3x^3 -3x^2-8x + 1$ is multiplied by $8x^4+2x^3 - 7x^2 + 3x + 4... | 37 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the coefficient of $x^3$ when $7x^4-3x^3 -3x^2-8x + 1$ is multiplied by $8x^4+2x^3 - 7x^2 + 3x + 4... | 37 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the coefficient of $x^3$ when $7x^4-3x^3 -3x^2-8x + 1$ is multiplied by $8x^4+2x^3 - 7x^2 + 3x + 4... | 37 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n若 $A+B=\\frac{2 \\pi}{3}$, 求 $\\cos ^{2} A+\\cos ^{2} B$ 的最小值和最大值，分别记为 $x$ 和 $y$。答案的形式分别为x = \\frac{m}{n}和... | 8 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n若 $A+B=\\frac{2 \\pi}{3}$, 求 $\\cos ^{2} A+\\cos ^{2} B$ 的最小值和最大值，分别记为 $x$ 和 $y$。答案的形式分别为x = \\frac{m}{n}和... | 8 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n若 $A+B=\\frac{2 \\pi}{3}$, 求 $\\cos ^{2} A+\\cos ^{2} B$ 的最小值和最大值，分别记为 $x$ 和 $y$。答案的形式分别为x = \\frac{m}{n}和... | 8 | {
"assistant_turn_index": 0,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n若 $A+B=\\frac{2 \\pi}{3}$, 求 $\\cos ^{2} A+\\cos ^{2} B$ 的最小值和最大值，分别记为 $x$ 和 $y$。答案的形式分别为x = \\frac{m}{n}和... | 8 | {
"assistant_turn_index": 1,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n若 $A+B=\\frac{2 \\pi}{3}$, 求 $\\cos ^{2} A+\\cos ^{2} B$ 的最小值和最大值，分别记为 $x$ 和 $y$。答案的形式分别为x = \\frac{m}{n}和... | 8 | {
"assistant_turn_index": 2,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n若 $A+B=\\frac{2 \\pi}{3}$, 求 $\\cos ^{2} A+\\cos ^{2} B$ 的最小值和最大值，分别记为 $x$ 和 $y$。答案的形式分别为x = \\frac{m}{n}和... | 8 | {
"assistant_turn_index": 0,
"total_assistant_turns": 1
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n若 $A+B=\\frac{2 \\pi}{3}$, 求 $\\cos ^{2} A+\\cos ^{2} B$ 的最小值和最大值，分别记为 $x$ 和 $y$。答案的形式分别为x = \\frac{m}{n}和... | 8 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n若 $A+B=\\frac{2 \\pi}{3}$, 求 $\\cos ^{2} A+\\cos ^{2} B$ 的最小值和最大值，分别记为 $x$ 和 $y$。答案的形式分别为x = \\frac{m}{n}和... | 8 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n若 $A+B=\\frac{2 \\pi}{3}$, 求 $\\cos ^{2} A+\\cos ^{2} B$ 的最小值和最大值，分别记为 $x$ 和 $y$。答案的形式分别为x = \\frac{m}{n}和... | 8 | {
"assistant_turn_index": 0,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the minimum possible perimeter of a right triangle with integer side lengths whose perimeter is eq... | 24 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the minimum possible perimeter of a right triangle with integer side lengths whose perimeter is eq... | 24 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the minimum possible perimeter of a right triangle with integer side lengths whose perimeter is eq... | 24 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the minimum possible perimeter of a right triangle with integer side lengths whose perimeter is eq... | 24 | {
"assistant_turn_index": 2,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the minimum possible perimeter of a right triangle with integer side lengths whose perimeter is eq... | 24 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nWhat is the minimum possible perimeter of a right triangle with integer side lengths whose perimeter is eq... | 24 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the number of ordered pairs $(a, b)$ of positive integers that are solutions of the following equatio... | 1 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the number of ordered pairs $(a, b)$ of positive integers that are solutions of the following equatio... | 1 | {
"assistant_turn_index": 2,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the number of ordered pairs $(a, b)$ of positive integers that are solutions of the following equatio... | 1 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the number of ordered pairs $(a, b)$ of positive integers that are solutions of the following equatio... | 1 | {
"assistant_turn_index": 0,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the number of ordered pairs $(a, b)$ of positive integers that are solutions of the following equatio... | 1 | {
"assistant_turn_index": 1,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the number of ordered pairs $(a, b)$ of positive integers that are solutions of the following equatio... | 1 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the number of ordered pairs $(a, b)$ of positive integers that are solutions of the following equatio... | 1 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the number of ordered pairs $(a, b)$ of positive integers that are solutions of the following equatio... | 1 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the number of ordered pairs $(a, b)$ of positive integers that are solutions of the following equatio... | 1 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn triangle $ABC$, lines $CE$ and $AD$ are drawn such that \\( \\frac{CD}{DB} = \\frac{3}{1} \\) and \\( \... | 5 | {
"assistant_turn_index": 0,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn triangle $ABC$, lines $CE$ and $AD$ are drawn such that \\( \\frac{CD}{DB} = \\frac{3}{1} \\) and \\( \... | 5 | {
"assistant_turn_index": 3,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn triangle $ABC$, lines $CE$ and $AD$ are drawn such that \\( \\frac{CD}{DB} = \\frac{3}{1} \\) and \\( \... | 5 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn triangle $ABC$, lines $CE$ and $AD$ are drawn such that \\( \\frac{CD}{DB} = \\frac{3}{1} \\) and \\( \... | 5 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn triangle $ABC$, lines $CE$ and $AD$ are drawn such that \\( \\frac{CD}{DB} = \\frac{3}{1} \\) and \\( \... | 5 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn triangle $ABC$, lines $CE$ and $AD$ are drawn such that \\( \\frac{CD}{DB} = \\frac{3}{1} \\) and \\( \... | 5 | {
"assistant_turn_index": 0,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn triangle $ABC$, lines $CE$ and $AD$ are drawn such that \\( \\frac{CD}{DB} = \\frac{3}{1} \\) and \\( \... | 5 | {
"assistant_turn_index": 4,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn triangle $ABC$, lines $CE$ and $AD$ are drawn such that \\( \\frac{CD}{DB} = \\frac{3}{1} \\) and \\( \... | 5 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe sales tax rate in Rubenenkoville is 6%. During a sale at the Bergville Coat Closet, the price of a coa... | 0 | {
"assistant_turn_index": 2,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe sales tax rate in Rubenenkoville is 6%. During a sale at the Bergville Coat Closet, the price of a coa... | 0 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe sales tax rate in Rubenenkoville is 6%. During a sale at the Bergville Coat Closet, the price of a coa... | 0 | {
"assistant_turn_index": 2,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe sales tax rate in Rubenenkoville is 6%. During a sale at the Bergville Coat Closet, the price of a coa... | 0 | {
"assistant_turn_index": 0,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe sales tax rate in Rubenenkoville is 6%. During a sale at the Bergville Coat Closet, the price of a coa... | 0 | {
"assistant_turn_index": 0,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIf $$\\begin{array}{@{}l@{\\;}l@{}l@{}l} && & P_b \\\\ & \\times & & P_b \\\\ \\cline{2-4} & & 3 & 1_b, \\... | 5 | {
"assistant_turn_index": 2,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIf $$\\begin{array}{@{}l@{\\;}l@{}l@{}l} && & P_b \\\\ & \\times & & P_b \\\\ \\cline{2-4} & & 3 & 1_b, \\... | 5 | {
"assistant_turn_index": 0,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIf $$\\begin{array}{@{}l@{\\;}l@{}l@{}l} && & P_b \\\\ & \\times & & P_b \\\\ \\cline{2-4} & & 3 & 1_b, \\... | 5 | {
"assistant_turn_index": 1,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIf $$\\begin{array}{@{}l@{\\;}l@{}l@{}l} && & P_b \\\\ & \\times & & P_b \\\\ \\cline{2-4} & & 3 & 1_b, \\... | 5 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIf $$\\begin{array}{@{}l@{\\;}l@{}l@{}l} && & P_b \\\\ & \\times & & P_b \\\\ \\cline{2-4} & & 3 & 1_b, \\... | 5 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(f_{1}(x)=\\sqrt{1-x}\\), and for integers \\(n \\geq 2\\), let \\(f_{n}(x)=f_{n-1}(\\sqrt{n^2 - x})... | -226 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(f_{1}(x)=\\sqrt{1-x}\\), and for integers \\(n \\geq 2\\), let \\(f_{n}(x)=f_{n-1}(\\sqrt{n^2 - x})... | -226 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(f_{1}(x)=\\sqrt{1-x}\\), and for integers \\(n \\geq 2\\), let \\(f_{n}(x)=f_{n-1}(\\sqrt{n^2 - x})... | -226 | {
"assistant_turn_index": 0,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(f_{1}(x)=\\sqrt{1-x}\\), and for integers \\(n \\geq 2\\), let \\(f_{n}(x)=f_{n-1}(\\sqrt{n^2 - x})... | -226 | {
"assistant_turn_index": 1,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(f_{1}(x)=\\sqrt{1-x}\\), and for integers \\(n \\geq 2\\), let \\(f_{n}(x)=f_{n-1}(\\sqrt{n^2 - x})... | -226 | {
"assistant_turn_index": 0,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(f_{1}(x)=\\sqrt{1-x}\\), and for integers \\(n \\geq 2\\), let \\(f_{n}(x)=f_{n-1}(\\sqrt{n^2 - x})... | -226 | {
"assistant_turn_index": 3,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(f_{1}(x)=\\sqrt{1-x}\\), and for integers \\(n \\geq 2\\), let \\(f_{n}(x)=f_{n-1}(\\sqrt{n^2 - x})... | -226 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(f_{1}(x)=\\sqrt{1-x}\\), and for integers \\(n \\geq 2\\), let \\(f_{n}(x)=f_{n-1}(\\sqrt{n^2 - x})... | -226 | {
"assistant_turn_index": 2,
"total_assistant_turns": 4
} |
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