data_source stringclasses 6
values | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | problem stringlengths 13 3.37k | prompt_messages listlengths 2 2 | gt stringlengths 1 461 |
|---|---|---|---|---|---|---|---|
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "56",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | How many different three-person sub-committees can be selected from a committee of eight people (the order of choosing the people does not matter)? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 56 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given two non-collinear vectors $\overrightarrow{a}$ and $\overrightarrow{b}$, their included angle is $\theta$, and $|\overrightarrow{a}| = 3$, $|\overrightarrow{b}| = 1$, and $x$ is a positive real number.
(1) If $\overrightarrow{a} + 2\overrightarrow{b}$ is perpendicular to $\overrightarrow{a} - 4\overrightarrow{b}$... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{1}{2} |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given $a > 0$ and $a \neq 1$, $b > 0$ and $b \neq 1$, if for any values of $a$ and $b$ within the given range, the function $y=x+\log_{a}(x-2)$ and the function $y=b^{x-c}+2$ always pass through the same fixed point, then the real number $c=$ ______. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 3 |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A rectangular piece of wood with a square cross-section has a surface area of 2448 square centimeters. From one end, a largest possible cube is sawed off, and the surface area of this cube is 216 square centimeters. The wood can yield at most ______ such cubes. (Note: Each sawing process wastes 2 millimeters of wood.) | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 15 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "(1,\\frac{\\pi}{2})",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In the polar coordinate system, the polar coordinates of the focus of the curve $p\cos^2\theta=4\sin\theta$ are \_\_\_\_\_\_\_\_\_\_\_\_ (Note: $p\geqslant 0,0\leqslant \theta < 2\pi $) | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | (1,\frac{\pi}{2}) |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "9.375 \\, \\text{days}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A team of 60 workers constructed a bridge in 5 days working at the same efficiency. If the subsequent team worked at 80% efficiency and consisted of 40 workers, how many days would it have taken this team to complete an identical bridge? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 9.375 \, \text{days} |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "(-1, +\\infty)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The range of the function $f\left(x\right)=\left\{\begin{array}{l}{{2}^{x}-1,x≤1}\\{{x}^{2}-2x,x＞1}\end{array}\right.$ is ______. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | (-1, +\infty) |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "x_1, x_2 = \\pm a \\sqrt{\\sqrt{2} + 1}, \\; y_1, y_2 = \\pm a \\sqrt{\\sqrt{2} - 1}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \[
\left\{
\begin{array}{l}
\log_{\sqrt{10}}\left(x^2 + y^2\right) = 2 \lg 2a + 2\log_{100}\left(x^2 - y^2\right) \\
xy = a^2
\end{array}
\right.
\] | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | x_1, x_2 = \pm a \sqrt{\sqrt{2} + 1}, \; y_1, y_2 = \pm a \sqrt{\sqrt{2} - 1} |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "1 + \\sqrt{3} + \\sqrt{6}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given a right triangle \( ABC \) with \(\angle A = 60^\circ\) and hypotenuse \( AB = 2 + 2\sqrt{3} \), a line \( p \) is drawn through vertex \( B \) parallel to \( AC \). Points \( D \) and \( E \) are placed on line \( p \) such that \( AB = BD \) and \( BC = BE \). Let \( F \) be the intersection point of lines \( A... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 1 + \sqrt{3} + \sqrt{6} |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "500",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given \( f(x)=\frac{a^{x}}{a^{x}+\sqrt{a}} \) (where \( a \) is a positive constant), find the value of \( f\left(\frac{1}{1001}\right)+f\left(\frac{2}{1001}\right)+\cdots+ f\left(\frac{1000}{1001}\right) \). | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 500 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "503",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The general term formula of the sequence $\{a_n\}$ is $a_n = \frac{1}{4}+\cos \frac{n\pi}{2}$. Let $S_n$ denote the sum of the first $n$ terms of the sequence. Find the value of $S_{2012}$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 503 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the sequence $\{a_n\}$ with the general term formula $a_n = -n^2 + 12n - 32$, determine the maximum value of $S_n - S_m$ for any $m, n \in \mathbb{N^*}$ and $m < n$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 10 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-\\frac{3}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In $\triangle ABC$, $b^{2}=ac$, and $a+c=3$, $\cos B= \frac{3}{4}$, then $\overset{→}{AB} \cdot \overset{→}{BC} =$______. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | -\frac{3}{2} |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-7",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $f(x) = -x^3 + 3x^2 + 9x + a$,
1. Find the intervals of monotonicity for $f(x)$.
2. If the maximum value of $f(x)$ on the interval $[-2,2]$ is $20$, find the minimum value of $f(x)$ on the same interval. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | -7 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "(-\\infty,-2) \\cup (2,+\\infty)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $f(x)$ be an odd function defined on $\mathbb{R}$ with $f(-2)=0$, and for $x > 0$, the inequality $\frac{xf'(x)-f(x)}{x^{2}} > 0$ always holds. Determine the solution set of the inequality $xf(x) > 0$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | (-\infty,-2) \cup (2,+\infty) |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "93",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $C$ be the greatest common factor and $D$ be the least common multiple of 18, 30, and 45. What is the value of $C + D$? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 93 |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "**B** From Point 0 to Point 3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If this path is to continue in the same pattern:
then which sequence of arrows goes from point $520$ to point $523$?
- **A** From Point 0 to Point 2
- **B** From Point 0 to Point 3
- **C** From Point 4 to Point 0
- **D** From Point 1 to Point 4 | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | **B** From Point 0 to Point 3 |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\left( -\\frac{3}{7}, \\frac{22}{7} \\right)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A line is expressed in the form
\[
\begin{pmatrix} 3 \\ 7 \end{pmatrix} \cdot \left( \begin{pmatrix} x \\ y \end{pmatrix} - \begin{pmatrix} -2 \\ 4 \end{pmatrix} \right) = 0.
\]
The equation of the line can be expressed in the form \( y = mx + b \). Enter the ordered pair \( (m,b) \). | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \left( -\frac{3}{7}, \frac{22}{7} \right) |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "y = -\\frac{3}{4}x + \\frac{75}{8}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The set of vectors $\mathbf{u}$ such that
\[\operatorname{proj}_{\begin{pmatrix} 3 \\ -4 \end{pmatrix}} \mathbf{u} = \begin{pmatrix} \frac{9}{2} \\ -6 \end{pmatrix}\]
lie on a line. Determine the equation of this line in the form "$y = mx + b$". | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | y = -\frac{3}{4}x + \frac{75}{8} |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "31\\%",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given a sample data with a size of 35, after grouping, the intervals and their corresponding frequencies are as follows: $[5, 10)$: 5; $[10, 15)$: 12; $[15, 20)$: 7; $[20, 25)$: 5; $[25, 30)$: 4; $[30, 35)$: 2. Determine the frequency of the sample in the interval $[20, +\infty)$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 31\% |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "a = -2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If the square root of a positive number $x$ is $2a-3$ and $5-a$, then $a=$____. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | a = -2 |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{147\\pi}{8} \\text{ sq cm}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A circular spinner for a game has a radius of 7 cm. The probability of winning on one spin of this spinner is $\frac{3}{8}$. What is the area, in sq cm, of the WIN sector? Express your answer in terms of $\pi$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{147\pi}{8} \text{ sq cm} |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{9}{64}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Two particles start from vertices A and B of equilateral triangle △ABC respectively. One moves at a uniform speed but the other moves twice as fast. Both follow the path A ⇒ B ⇒ C ⇒ A. The slower particle starts from A and the faster from B. The midpoint of the line segment connecting these two particles traces out a p... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{9}{64} |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "4\\pi",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In the polar coordinate system, find the area enclosed by the curve $\rho = 4\cos\theta$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 4\pi |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "53.125\\pi",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In the diagram, each circle is divided into two equal areas and $O$ is the center of the larger circle. The area of the larger circle is $100\pi.$ What is the total area of the shaded regions? [asy]
size(100);
import graph;
fill(Arc((0,0),2,180,360)--cycle,mediumgray);fill(Arc((0,1),1,0,180)--cycle,mediumgray);
draw(Ci... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 53.125\pi |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{5}{12}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | When a red die and a blue die are thrown at the same time, let event $M$ be "the number of points facing up on the red die is a multiple of 3", and $N$ be "the sum of the points on both dice is greater than 8". Calculate $P(N|M)$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{5}{12} |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate the largest integer $n$ such that $\binom{12}{5} + \binom{12}{6} = \binom{13}{n}$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 7 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{7}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given vectors $\overrightarrow {a}$ and $\overrightarrow {b}$ that satisfy $|\overrightarrow {a}| = 1$, $|\overrightarrow {b}| = 2$, and $|\overrightarrow {a} - 2\overrightarrow {b}| = \sqrt{10}$, find the value of $\overrightarrow {a} \cdot \overrightarrow {b}$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{7}{4} |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $a,$ $b,$ $c,$ and $d$ be positive real numbers. Find the minimum value of
\[
\frac{a}{b} + \frac{b}{c} + \frac{c}{d} + \frac{d}{a}.
\] | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 4 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-\\frac{3}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that $\sin \alpha = \frac{3}{5}$, and $\alpha \in (\frac{\pi}{2}, \pi)$, find the value of $\tan \alpha$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | -\frac{3}{4} |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "1.33",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Moe uses a mower to cut his rectangular 100-foot by 120-foot lawn. The swath he cuts is 30 inches wide, but he overlaps each cut by 6 inches to ensure no grass is missed. He walks at the rate of 4500 feet per hour while pushing the mower. Calculate the time it will take him to mow the lawn. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 1.33 |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "132",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | How many distinct, natural-number factors does $4^5 \cdot 5^3 \cdot 7^2$ have? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 132 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "[-4, -1] \\cup [1, 2]",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that the domain of the function $f(x)$ is $R$, the graph of $f(x-1)$ is symmetric about the point $(1,0)$, $f(3)=0$, and for any $x_{1}$, $x_{2}\in (-\infty,0)$, $x_{1}\neq x_{2}$, it satisfies $\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}＜0$. Then solve the inequality $\left(x-1\right)f(x+1)\geqslant 0$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | [-4, -1] \cup [1, 2] |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the radius of the circle whose center lies on the line $2x+y=0$ and passes through the points $A(1,3)$ and $B(4,2)$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 5 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The line $l_{1}$: $ax+3y+1=0$, and the line $l_{2}$: $2x+(a+1)y+1=0$. If $l_{1} \parallel l_{2}$, then $a=$ __________. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | -3 |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{\\pi + \\sqrt{\\pi^2 + 4\\pi + 8}}{4 - 2\\pi}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | C is a circle of radius \(a\) whose center lies at a distance \(b\) from the coplanar line \(L\). C is rotated through \(\pi\) about \(L\) to form a solid whose center of gravity lies on its surface. Find \(\frac{b}{a}\). | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{\pi + \sqrt{\pi^2 + 4\pi + 8}}{4 - 2\pi} |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "25^\\circ",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A line passing through vertex $A$ of triangle $ABC$ intersects side $BC$ at point $M$. Here, $BM = AB$, $\angle BAM = 35^\circ$, and $\angle CAM = 15^\circ$.
Find the angles of triangle $ABC$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 25^\circ |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{4095}{4096}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What is the probability that when we roll five fair 8-sided dice, they won't all show the same number? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{4095}{4096} |
numina_aops_forum | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\sqrt{4 + \\sqrt{3}}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Four copies of an acute scalene triangle $\mathcal T$ , one of whose sides has length $3$ , are joined to form a tetrahedron with volume $4$ and surface area $24$ . Compute the largest possible value for the circumradius of $\mathcal T$ . | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \sqrt{4 + \sqrt{3}} |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\pm 2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that two different square roots of a certain positive number are $3a-14$ and $a-2$; and the cube root of $b-15$ is $-3$.
$(1)$ Find the values of $a$ and $b$;
$(2)$ Find the square root of $4a+b$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \pm 2 |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "31",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | On an island, there are only 50 knights, who always tell the truth, and 15 civilians, who can either tell the truth or lie. A forgetful professor, who came to the island to give a lecture, forgot what color hat he is wearing. What is the minimum number of local inhabitants that the professor needs to ask about the colo... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 31 |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{99}{7}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate \(x\) if the arithmetic mean of the following five expressions is 30:
$$x + 10 \hspace{.5cm} 20 \hspace{.5cm} 3x \hspace{.5cm} 15 \hspace{.5cm} 3x + 6$$ | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{99}{7} |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\left( 3, \\frac{\\pi}{3}, \\cos^{-1}\\left(\\frac{2}{3}\\right) \\right)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Convert the point $(1, \sqrt{3}, 2)$ in rectangular coordinates to spherical coordinates. Enter your answer in the form $(\rho,\theta,\phi),$ where $\rho > 0,$ $0 \le \theta < 2 \pi,$ and $0 \le \phi \le \pi.$ | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \left( 3, \frac{\pi}{3}, \cos^{-1}\left(\frac{2}{3}\right) \right) |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "1440",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the product of the greatest common divisor and the least common multiple of $24$ and $60$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 1440 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "a=3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $f(x)= \begin{cases} x+ \frac {a}{x}-3,x\geqslant 1 \\ \log_{10} (x^{2}+1),x < 1 \end{cases}$, if $f(1)=f(-3)$, find the value of $a$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | a=3 |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "2011^{2009} \\cdot \\left(1005^{2011} - 1004^{2011}\\right)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let \( z=\cos \frac{2 \pi}{2011}+i \sin \frac{2 \pi}{2011} \), and let
\[ P(x)=x^{2008}+3 x^{2007}+6 x^{2006}+\ldots + \frac{2008 \cdot 2009}{2} x+\frac{2009 \cdot 2010}{2} \]
for all complex numbers \( x \). Evaluate \( P(z) P\left(z^{2}\right) P\left(z^{3}\right) \ldots P\left(z^{2010}\right) \). | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 2011^{2009} \cdot \left(1005^{2011} - 1004^{2011}\right) |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $h(x) = x^5 + x^4 + x^3 + x^2 + x + 1.$ What is the remainder when the polynomial $h(x^{10})$ is divided by the polynomial $h(x)$? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 6 |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What is the sum of all integer values \( n \) for which \( \binom{15}{n} + \binom{15}{7} = \binom{16}{8} \)? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 8 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that $f(x)$ is an even function defined on the real number domain and when $x \leq 0$, $f(x) = (x+1)^3e^{x+1}$, calculate the number of extreme points of the function $f(x)$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 3 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given: $y= \sqrt{x-2} + \sqrt{2-x} + 1$, find the value of the expression $(\sqrt{48y} + \sqrt{8x})(4\sqrt{3y} - 2\sqrt{2x}) - xy$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 30 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "(0, \\frac{1}{2})",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $f(x)=x(\ln x-ax)$ has two extreme points, determine the range of the real number $a$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | (0, \frac{1}{2}) |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that $e$ is the base of the natural logarithm, let the function $f(x) = xe^x$. Determine the nature of the point $x = 1$ with respect to the function $f(x)$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | -1 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "x - y + 3 = 0",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If a line passing through point $A(1,4)$ has a sum of intercepts on the two coordinate axes equal to zero, determine the equation of the line. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | x - y + 3 = 0 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given two non-zero vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ that satisfy $|\overrightarrow{a}+\overrightarrow{b}|=|\overrightarrow{a}-\overrightarrow{b}|=2|\overrightarrow{a}|$, find the angle between the vectors $\overrightarrow{a}+\overrightarrow{b}$ and $\overrightarrow{a}-\overrightarrow{b}$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 120 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given \((1+x)^n = a_0 + a_1x + a_2x^2 + a_3x^3 + \ldots + a_nx^n\), if \(\frac{a_2}{a_3} = \frac{1}{3}\), then \(n=\) ______. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 9 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "①②",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | For the quadratic function $y=mx^{2}-(4m+1)x+3m+3$ where $m \lt 0$, the following statements are made:<br/>① When $x \gt 2$, $y$ decreases as $x$ increases;<br/>② Regardless of the value of $m$, the graph of the function must pass through the points $(1,2)$ and $(3,0)$;<br/>③ The distance between the two intersection p... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | ①② |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "880",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What is the largest three-digit multiple of 8 whose digits' sum is 16? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 880 |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "x=18^\\circ, 45^\\circ, 90^\\circ, 135^\\circ, 162^\\circ, 210^\\circ, 225^\\circ, 234^\\circ, 270^\\circ, 306^\\circ, 315^\\circ, 330^\\circ",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Solve the following equation:
$$
\cos x+\cos 3 x=\frac{1}{2} \tan 4 x
$$ | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | x=18^\circ, 45^\circ, 90^\circ, 135^\circ, 162^\circ, 210^\circ, 225^\circ, 234^\circ, 270^\circ, 306^\circ, 315^\circ, 330^\circ |
numina_amc_aime | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "3^4",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | $3^3+3^3+3^3=$ | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 3^4 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If point P $(2a+1, -3a)$ is symmetric to point $P_1 (1, 3-b)$ with respect to the x-axis, then $b^a = \ $. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 1 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If the minimum value of the function $f(x) = x^2 + 4x + 5 - c$ is $2$, then the minimum value of the function $y = f(x - 3)$ is $\_\_\_\_\_\_.$ | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 2 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "[2,+\\infty)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The range of the function $y=x^2-4x+6$ is. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | [2,+\infty) |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that the terms of the geometric sequence $\\{a_{n}\\}$ are all positive numbers, and $a_{4}a_{10}=16$, find $a_{7}=$ _____. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 4 |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\$74622",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Tim wants to invest some money in a bank which compounds semi-annually with an annual interest rate of \(10\%\). To the nearest dollar, how much money should he invest if he wants a total of \( \$100,000 \) at the end of \(3\) years? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \$74622 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "A \\cup B = \\{x \\mid x \\leq -\\sqrt{2} \\text{ or } x \\geq 1\\}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the sets $A = \{x \mid x^2 - 2 \geq 0\}$ and $B = \{x \mid x^2 - 4x + 3 \leq 0\}$, determine the union $A \cup B$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | A \cup B = \{x \mid x \leq -\sqrt{2} \text{ or } x \geq 1\} |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "(-5,0)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If point $P(m-3,2+m)$ lies on the $x$-axis, then the coordinates of point $P$ are ______. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | (-5,0) |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "T_n = 4 - \\frac{n+2}{2^{n-1}}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given an arithmetic sequence $\{a_n\}$ with $a_1=1$ and $a_5=5$, and a geometric sequence $\{b_n\}$ whose sum of the first $n$ terms is $S_n = 2 - \frac{1}{2^{n-1}}$ $(n \in \mathbb{N}^*)$.
(1) Find the general term formulas for sequences $\{a_n\}$ and $\{b_n\}$.
(2) If $c_n = a_nb_n$ $(n=1, 2, 3, \ldots)$ and $T_n... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | T_n = 4 - \frac{n+2}{2^{n-1}} |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "15625 \\text{ square feet}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Brian is tasked with constructing a fence around a rectangular dog park. He has exactly 500 feet of fencing available. The fence must enclose all four sides of the park, and regulatory guidelines require that the length of the park must be at least 100 feet and the width must be at least 60 feet. Brian wants the enclos... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 15625 \text{ square feet} |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "x + y - z = 0",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the equation of the plane passing through $(0,2,2)$ and $(2,0,2),$ and which is perpendicular to the plane $2x - y + 3z = 7.$ Enter your answer in the form \[Ax + By + Cz + D = 0,\] where $A,$ $B,$ $C,$ $D$ are integers such that $A > 0$ and $\gcd(|A|,|B|,|C|,|D|) = 1.$ | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | x + y - z = 0 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If the solution set of the inequality $tx^2-6x+t^2<0$ with respect to $x$ is $(-\infty, a) \cup (1, +\infty)$, then the value of $a$ is \_\_\_\_\_\_. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | -3 |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "2\\sqrt{399}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Triangle $PQR$ is a right triangle with legs $PQ$ and $PR$. Points $M$ and $N$ lie on legs $PQ$ and $PR$, respectively, such that $PM:MQ = PN:NR = 1:3$. If $QN = 20$ units, and $MR = 36$ units, what is the length of hypotenuse $QR$? Express your answer in simplest radical form. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 2\sqrt{399} |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\sqrt{41}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $C$ be the vertex of the graph of the equation $y = x^2 + 6x + 13$. Let $D$ be the vertex of the graph of the equation $y = -x^2 + 2x + 8$. What is the distance between $C$ and $D$? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \sqrt{41} |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "2\\sqrt{61}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A cylinder has a radius of 5 cm and a height of 12 cm. What is the longest segment, in centimeters, that fits inside the cylinder? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 2\sqrt{61} |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "27",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate three-fifths of the product of 5 and 9. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 27 |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "3 \\text{ colors}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | On a sheet of paper, 25 points are marked as the centers of the cells of a $5 \times 5$ square grid. The points are colored in several colors. It is known that no three points of the same color lie on a single straight line (whether vertical, horizontal, or diagonal). What is the minimum number of colors that could hav... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 3 \text{ colors} |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-1 \\ or \\ 2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $f(x)= \begin{cases} \log_{2}x,x > 0 \\ x^{2},x\leqslant 0 \end{cases}$, if $f(4)=2f(a)$, find the value of the real number $a$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | -1 \ or \ 2 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{\\pi}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The graph of the function $f(x) = \sin x + \cos x$ is shifted to the right by $\varphi$ ($\varphi > 0$) units, and the resulting graph is symmetric about the origin. Determine the minimum value of $\varphi$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{\pi}{4} |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the coefficient of $x^3$ in the expansion of $\left( \sqrt{x} - \frac{2}{x} + 1 \right)^7$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 7 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "( \\\\dfrac {8}{13}, \\\\dfrac {5}{8})∪( \\\\dfrac {8}{5}, \\\\dfrac {13}{8})",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that the set $${φ|f(x)=\\sin \[(x-2φ)π\]+\\cos \[(x-2φ)π\]}$$ is an odd function, and the number of subsets for which $$|\\log \_{a}φ| < 1$$ is 4, find the range of values for $a$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | ( \\dfrac {8}{13}, \\dfrac {5}{8})∪( \\dfrac {8}{5}, \\dfrac {13}{8}) |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "25^\\circ",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What is the measure, in degrees, of the acute angle formed by the minute hand and the hour hand on a standard clock when it indicates $10$:$50$? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 25^\circ |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\sqrt{2}+1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $f(x)=\log_{a} \frac{2-x}{b+x} (0 < a < 1)$ is an odd function, when $x \in (-2,2a)$, the range of the function $f(x)$ is $(-\infty,1)$, then the sum of the real numbers $a+b=$ __________. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \sqrt{2}+1 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\pm 2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given sets $A=\{-1, 3, m^2\}$ and $B=\{3, 4\}$, if $B \subseteq A$, then $m=$? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \pm 2 |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Mary had ten pieces of paper. Some of them were squares, and the rest were triangles. She cut three squares diagonally from corner to corner. She then found that the total number of vertices of the 13 pieces of paper was 42. How many triangles did she have before making the cuts?
A) 8
B) 7
C) 6
D) 5
E) 4 | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 4 |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "3.391",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Determine the value of $x$ if $5(x - 10) = 6(3 - 3x) + 10$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 3.391 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "a = 3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the equation of a circle $x^{2}+y^{2}-2ax+4y-6=0$, if the center of the circle lies on the line $x+2y+1=0$, what is the value of the real number $a$? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | a = 3 |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "4275",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Sets $C$ and $D$, shown in a Venn diagram, are such that the total number of elements in set $C$ is three times the total number of elements in set $D$. Altogether, there are 4500 elements in the union of $C$ and $D$, and their intersection has 1200 elements. What is the total number of elements in set $C$? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 4275 |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "4x - 3y + 5 = 0",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the equation of the line that is symmetric to the line $3x - 4y + 5 = 0$ with respect to the line $x + y = 0$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 4x - 3y + 5 = 0 |
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