data_source stringclasses 6
values | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | problem stringlengths 14 4.91k | prompt_messages listlengths 2 2 | gt stringlengths 1 936 |
|---|---|---|---|---|---|---|---|
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": "788",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the quadratic function $y=3x^2 - 12x + 800$, find the minimum value of $y$ under the condition that $x$ is a non-negative integer. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 788 |
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}{8}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given points A(1, 0), B(0, 1), and C(2sinθ, cosθ).
(1) If $|\overrightarrow{AC}| = |\overrightarrow{BC}|$, find the value of $\frac{\sin\theta + 2\cos\theta}{\sin\theta - \cos\theta}$;
(2) If $(\overrightarrow{OA} + 2\overrightarrow{OB}) \cdot \overrightarrow{OC} = 1$, where O is the origin, find the value of $\sin\the... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | -\frac{3}{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": "\\frac{1}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If the product of the polynomial $x-2$ and $x^{2}+mx+1$ does not contain a linear term in $x$, find the value of $m$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \frac{1}{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": "203",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | There are three simplified proper fractions whose numerators have a ratio of $3: 2: 4$ and whose denominators have a ratio of $5: 9: 15$. After adding these three fractions and simplifying the result, the sum is $\frac{28}{45}$. What is the sum of the denominators of the three fractions? | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 203 |
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": "33",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Kiran needs to solve the quadratic equation \(16x^2 + 32x - 512 = 0\) using the method of completing the square. In this process, she derives an equivalent equation \((x + p)^2 = q\), where \(p\) and \(q\) are constants. Determine \(q\). | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 33 |
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": "[-1,0]",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that $f(x)$ is an even function defined on the real number line $\mathbb{R}$, and $f(x)$ is an increasing function on the interval $[0, +\infty)$, if for any $x \in [1,2]$, the inequality $f(ax+1) \leqslant f(x-3)$ is always true, then the range of values for the real number $a$ 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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | [-1,0] |
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": "7",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The motion equation of an object is $s=1-t+t^2$, determine the instantaneous velocity of the object at $t=4$ seconds. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 7 |
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": "C) 76",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Determine the number obtained from the last two nonzero digits of $100!$.
A) 12
B) 32
C) 76
D) 68
E) 87 | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | C) 76 |
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{x^2}{16} + \\frac{y^2}{12} = 1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given an ellipse $C:\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1(a\gt b\gt 0)$ with the right focus $F(c,0)$ and the right vertex $A$, where point $P$ is any point on the ellipse other than point $A$, the maximum area of $\triangle APF$ is $\frac{\sqrt{3}{{b}^{2}}}{6}$.
1. Find the eccentricity of the ellipse $C$... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \frac{x^2}{16} + \frac{y^2}{12} = 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|-2, -1, 0, 1, 2\\}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The set $\{x|-3 < x < 3 \text{ and } x \in \mathbb{Z}\}$ can be represented by listing method as \_\_\_\_\_\_. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \{x|-2, -1, 0, 1, 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": "6",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the numbers \(\log _{\sqrt{2 x-8}}(x-4), \log _{(x-4)^{2}}(5 x-26), \log _{\sqrt{5 x-26}}(2 x-8)\). For which values of \(x\) are two of these numbers equal, and the third one is greater by 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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 6 |
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"
} | Given the function $f(x) = \begin{cases} 2^{x}+1, & x < 1\\ x^{2}+ax, & x\geqslant 1 \end{cases}$, if $f[f(0)]=4a$, then the real number $a$ is equal to $\_\_\_\_\_\_$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 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"
} | The complex number $m^2-9+(m+3)i$ is a pure imaginary number, then the value of the real number $m$ 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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 3 |
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": "C) 250",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Mrs. Johnson has two grandchildren, who ring her on a regular schedule. One grandchild calls her every 5 days and the other calls her every 7 days. Both grandchildren called her initially on January 1, 2022. Determine the total number of days in the year 2022 that Mrs. Johnson did not receive a phone call from either g... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | C) 250 |
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": "15\\sqrt{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In a right prism with isosceles triangular bases, given the sum of the areas of three mutually adjacent faces (two lateral faces and one base) is 30, find the maximum volume of the prism. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 15\sqrt{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-i",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given $\frac{(1-i)^2}{z}=1+i$ (where $i$ is the imaginary unit), find the complex number $z$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | -1-i |
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"
} | A whole block of modeling clay is a right rectangular prism eight inches by three inches by two inches. How many whole blocks are needed to mold a cylindrical sculpture ten inches high and six inches in diameter? | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 6 |
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 \\sqrt {2}+2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In the Cartesian coordinate system, the parametric equation of line $l$ is
$$
\begin{cases}
x=-5+ \frac { \sqrt {2}}{2}t \\
y=-1+ \frac { \sqrt {2}}{2}t
\end{cases}
$$
where $t$ is the parameter. Now, taking the origin as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is estab... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 3 \sqrt {2}+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": "24\\pi",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A right triangle $\triangle ABC$ has sides $AC=3$, $BC=4$, and $AB=5$. When this triangle is rotated around the right-angle side $BC$, the surface area of the resulting solid 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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 24\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": "(0, \\frac{2}{3}) \\cup (1, +\\infty)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given \(\log_a \frac{2}{3} < 1\), determine the range 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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | (0, \frac{2}{3}) \cup (1, +\infty) |
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": "C) 10",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Determine the smallest value of $N$ such that when $(a+b+c+d+e+1)^N$ is expanded and like terms are combined, it contains exactly 252 terms that include all five variables $a, b, c, d, e$, each to some positive power.
A) 8
B) 9
C) 10
D) 11
E) 12 | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | C) 10 |
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{3}{5}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Two distinct numbers are selected simultaneously and at random from the set $\{1, 2, 3, 6, 9\}$. What is the probability that the smaller one divides the larger one? Express your answer as a common fraction. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \frac{3}{5} |
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": "75^\\circ",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $ABC$ be a triangle, and let $P$ be a point on side $BC$ such that $\frac{BP}{PC}=\frac{1}{2}$ . If $\measuredangle ABC$ $=$ $45^{\circ}$ and $\measuredangle APC$ $=$ $60^{\circ}$ , determine $\measuredangle ACB$ without trigonometry. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 75^\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": "13",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What is the positive difference between the median and the mode of the data given in the stem and leaf plot below? In this plot $5|8$ represents $58.$
\begin{tabular}{|c|c|}\hline
\textbf{Tens} & \textbf{Units} \\ \hline
1 & $7 \hspace{2mm} 7 \hspace{2mm} 7 \hspace{2mm} 9$ \\ \hline
2 & $1 \hspace{2mm} 1 \hspace{2mm} ... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 13 |
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": "0.128",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In a certain competition, the rules are as follows: among the 5 questions preset by the organizer, if a contestant can answer two consecutive questions correctly, they will stop answering and advance to the next round. Assuming the probability of a contestant correctly answering each question is 0.8, and the outcomes o... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 0.128 |
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"
} | A person's commute times (in minutes) for 5 days were $m$, $n$, $5$, $6$, and $4$. It is known that the average of this set of data is $5$, and the variance is $2$. Find the value of $|m-n|$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 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": "\\text{The maximum distance is } \\frac{2\\sqrt{10} + 6\\sqrt{5}}{5}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In polar coordinates, the polar equation of curve C is given by $$\rho^{2} = \frac{4}{4\sin^{2}\theta + \cos^{2}\theta}$$, and the polar equation of the line l is $$\rho(\cos\theta + 2\sin\theta) + 6 = 0$$.
(I) Find the Cartesian coordinate equation of curve C and its eccentricity $e$.
(II) Point P is a moving point on... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \text{The maximum distance is } \frac{2\sqrt{10} + 6\sqrt{5}}{5} |
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{89}{12}\\pi",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Spot's doghouse has a regular hexagonal base that measures two yards on each side. He is tethered to a vertex with a three-yard rope. An overhang adjacent to the doghouse creates a shaded region that Spot can also explore. This shaded region is a sector with an angle of \(90^\circ\) and radius of 1 yard located at a ve... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \frac{89}{12}\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{\\sqrt{10}}{5}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If $\theta \in (0, \frac{\pi}{2})$, $\tan \theta = \frac{1}{3}$, then $\sin \theta - \cos \theta = \_\_\_\_\_\_$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | -\frac{\sqrt{10}}{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": "\\text{④⑥}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given three different planes $\alpha$, $\beta$, $\gamma$, and lines $a$, $b$, $c$ respectively in planes $\alpha$, $\beta$, $\gamma$. If $\beta \perp \gamma$ and $\alpha$ intersects $\gamma$ but not perpendicularly, then which of the following statements are true?
① $\forall b \subset \beta$, $b \perp \gamma$ 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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \text{④⑥} |
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{2}{11}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given a sequence $\{a_n\}$ with $a_1=1$ and $a_{n+1}= \frac{2a_n}{a_n+2}$, find the value of $a_{10}$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \frac{2}{11} |
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\\sqrt{2 - \\sqrt{2}}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A circle $U$ has a circumference of $18\pi$ inches, and segment $AB$ is a diameter. If the measure of angle $UAV$ is $45^{\circ}$, what is the length, in inches, of segment $AV$? | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 9\sqrt{2 - \sqrt{2}} |
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": "2\\sqrt{7}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A triangle has two medians of lengths 5 inches and 9 inches which are perpendicular to each other, and the area of the triangle is $6 \sqrt{35}$ square inches. Calculate the length of the third median.
A) $3\sqrt{7}$
B) $2\sqrt{7}$
C) $5\sqrt{7}$
D) $4\sqrt{7}$
E) $6\sqrt{7}$ | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 2\sqrt{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": "2\\sqrt{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Two rays with common endpoint $O$ form a $45^\circ$ angle. Point $A$ lies on one ray, point $B$ on the other ray, and $AB=2$. What is the maximum possible length of $\overline{OB}$? | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 2\sqrt{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": "f(x) = x(x+1)(x-1)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Write down a function $f\left(x\right)=\_\_\_\_\_\_$ that satisfies the following three properties.<br/>① $f\left(x\right)$ is an odd function; ② $f\left(x\right)$ is monotonically increasing in $\left(2,+\infty \right)$; ③ $f\left(x\right)$ has exactly $3$ zeros. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | f(x) = x(x+1)(x-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": "\\dfrac{3 \\sqrt{3}}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In triangle $ABC$, the sides opposite to angles $A$, $B$, and $C$ are respectively $a$, $b$, and $c$. The vector $\vec{m}=(a, \sqrt{3}b)$ is parallel to the vector $\vec{n}=(\cos A,\sin B)$.
$(1)$ Find $A$;
$(2)$ If $a= \sqrt{7}$ and $b=2$, find the area 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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \dfrac{3 \sqrt{3}}{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"
} | Kirra has 7 cards but no envelopes and each package comes with 10 envelopes. Determine the smallest number of packages that Kirra needs to buy to have more envelopes than cards. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 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": "27",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What is the perimeter of a regular nonagon (9-sided polygon) where each side measures 3 units? | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 27 |
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": "24",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | On the ellipse $\dfrac{x^2}{49} + \dfrac{y^2}{24} = 1$, a point $P$ forms perpendicular lines with the two foci $F_1$ and $F_2$ of the ellipse. Find the area of $\triangle PF_1F_2$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 24 |
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": "50",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Jenny and Kenny are walking in the same direction on parallel paths that are 300 feet apart. This time, a square building with sides of 100 feet is centered midway between their paths. If Kenny is walking at a speed of 4 feet per second and Jenny at a speed of 2 feet per second, at what time $t$ will they be able to se... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 50 |
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{\\sqrt{13}}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the hyperbola $\frac{y^{2}}{9} - \frac{x^{2}}{b^{2}} = 1 (b > 0)$ with asymptotes $3x \pm 2y = 0$, determine its eccentricity. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \frac{\sqrt{13}}{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": "\\sqrt {7}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In acute triangle ABC, a, b, and c are the sides opposite to angles A, B, and C respectively. If 2asinB = $\sqrt {3}$b, b + c = 5, and bc = 6, find 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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \sqrt {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{2\\pi}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $f(x)=Asin(ωx+\frac{π}{6})\left(A \gt 0,\omega\ \ \gt 0\right)$, which can only satisfy any two of the following three conditions: ① the maximum value of the function $f\left(x\right)$ is $2$; ② the graph of the function $f\left(x\right)$ can be obtained by shifting the graph of $y=\sqrt{2}sin(x-\fra... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \frac{2\pi}{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": "15",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Of the 80 students in the drama club, 50 take mathematics, 40 take physics, and 25 students take both mathematics and physics. How many drama club students take neither mathematics nor physics? | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 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",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given an ellipse $C: \frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1\ (a > b > 0)$ with one of its vertices at $A(2,0)$, an eccentricity of $\frac{\sqrt{2}}{2}$, and a line $y=k(x-1)$ intersecting the ellipse $C$ at two distinct points $M$ and $N$.
1. Find the equation of the ellipse $C$.
2. Find the value of the real numb... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | ±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": "11",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate $\lfloor |-5.7| \rfloor + |\lfloor -5.7 \rfloor|$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 11 |
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",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let \(a\) and \(b\) be positive real numbers with \(a \ge b\). Consider the system of equations:
\[ a^2 + y^2 = b^2 + x^2 = (a - x)^2 + (b + y)^2 \]
with the condition that there exists a solution \((x, y)\) such that \(0 \leq x < a\) and \(0 \leq y < b\). Determine the maximum possible value of \(\frac{a}{b}\), denote... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 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": "-x^2 + 3x - \\frac{3}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate \[x(3-4x) + 2x^2(x-1)\] ÷ (-2x) | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | -x^2 + 3x - \frac{3}{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{32}{1089}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate the product of $0.\overline{08}$ and $0.\overline{36}$ and express it as a common fraction. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \frac{32}{1089} |
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{1}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What is the probability that a positive integer less than or equal to 36 is a factor of 36? Express your answer as a common fraction. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \frac{1}{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": "3x + y + 1 = 0",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The graph of the function $f(x) = a^{x+1} + 1$ ($a > 0$ and $a \neq 1$) always passes through a fixed point A, and point A lies on the line $l: bx + y + 1 = 0$. Then, the equation of line $l$ 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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 3x + y + 1 = 0 |
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{28}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the maximum value of
\[
\frac{2x + 3y + 4}{\sqrt{2x^2 + 3y^2 + 5}}
\]
over all real numbers \(x\) and \(y\). | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \sqrt{28} |
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(1+0.03)^5",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | When a deposit of 20,000 yuan is made into a bank account with an annual interest rate of 3%, calculate the total amount of principal and interest withdrawn after 5 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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 2(1+0.03)^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": "\\{x|x<3\\}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given $M=\{x|x^2-4x+3<0\}$ and $N=\{x|2x+1<5\}$, then $M\cup N=$ ? | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \{x|x<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": "1320",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In a committee arrangement, there are seven women and three men. Women sit on seven indistinguishable rocking chairs, men sit on three indistinguishable stools, and additionally, there is one unique chair with armrests that can be occupied by anyone. In how many ways can the rocking chairs, stools, and the unique chair... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 1320 |
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{3}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $x,$ $y,$ $z$ be positive real numbers such that $x + y + z = 3.$ Find the minimum value of
\[\frac{1}{x + 3y} + \frac{1}{y + 3z} + \frac{1}{z + 3x}.\] | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \frac{3}{4} |
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": "n-1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Isabel wants to partition the set $\mathbb{N}$ of the positive integers into $n$ disjoint sets $A_{1}, A_{2}, \ldots, A_{n}$ . Suppose that for each $i$ with $1\leq i\leq n$ , given any positive integers $r, s\in A_{i}$ with $r\neq s$ , we have $r+s\in A_{i}$ . If $|A_{j}|=1$ for some $j$ , find the grea... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 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": "2^4 \\cdot 3^2 \\cdot 5^3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the least common multiple (LCM) of 48, 180, and 250, then factor the result into its prime factors. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 2^4 \cdot 3^2 \cdot 5^3 |
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": "1000000",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What is the greatest product obtainable from two integers whose sum is 2000? | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 1000000 |
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"
} | Given that the function $f(x)$ satisfies $f(x+3) = -f(x)$ for any real number $x$, and given $f(4) = -2$, find the value of $f(2011)$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 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": "1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | For which positive integers \( n \) does the number \( n^{2} + 1 \) divide \( n + 1 \)? | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 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": "-3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If the graph of the function $y=\frac{k}{x}$ passes through the point $\left(3,-1\right)$, find the value of $k$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | -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": "2\\pi",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that the radius of the cone base is $1$ and the height is $\sqrt{3}$, find the lateral area of the cone. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 2\pi |
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": "38",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In the diagram below, how many distinct paths are there from January 1 to December 31, moving from one adjacent dot to the next either to the right, down, or diagonally down to the right?
[asy]
size(340);
int i, j;
for(i = 0; i<10; i = i+1) {
for(j = 0; j<5; j = j+1) {
if(10*j + i == 11 || 10*j + i == 12 || 10*j + i =... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 38 |
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": "(6, 9), (7, 3), (8, 1), (9, 0), (11, -1), (17, -2), (4, -15), (3, -9), (2, -7), (1, -6), (-1, -5), (-7, -4)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Solve the equation in integers:
$$
xy + 3x - 5y = -3
$$ | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | (6, 9), (7, 3), (8, 1), (9, 0), (11, -1), (17, -2), (4, -15), (3, -9), (2, -7), (1, -6), (-1, -5), (-7, -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": "\\sqrt{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and $c(a\cos B-b\cos A)=b^{2}$. Find the value of $\frac{\sin A}{\sin B}$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \sqrt{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{1}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The imaginary part of the complex number $z= \frac{i^{5}}{1-i}$ (where $i$ is the imaginary unit), calculate its value. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \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 $0 < α < \frac{π}{2}$ and $\frac{π}{2} < β < π$, with $\cos(α + \frac{π}{4}) = \frac{1}{3}$ and $\cos(\frac{π}{4} - \frac{β}{2}) = \frac{\sqrt{3}}{3}$,
1. Find the value of $\cos β$;
2. Find the value of $\cos(2α + β)$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | -1 |
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": "300",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If the sum of the first $3n$ positive integers is $150$ more than the sum of the first $n$ positive integers, find the sum of the first $4n$ positive integers. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 300 |
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": "②③④",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $f(x) = e^x + a \ln x$ with a domain of $(0, +\infty)$, the following propositions are provided regarding the function $f(x)$:
$①$ When $a = 1$, $f(x)$ has a maximum value;
$②$ When $a = -1$, for any $x > 0$, $f(x) > 0$;
$③$ For any $a > 0$, $f(x)$ is an increasing function on $(0, +\infty)$;
$④$... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | ②③④ |
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}{12}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate:<br/>$(1)(-6)+(-13)$;<br/>$(2)\frac{3}{5}+(-\frac{3}{4})$;<br/>$(3)4.7+(-0.8)+5.3+(-8.2)$;<br/>$(4)(-\frac{1}{6})+(\frac{1}{3})+(-\frac{1}{12})$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \frac{1}{12} |
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|0 < x < 3\\}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The solution set of the inequality $ax^{2}+bx+c > 0$ is $\{x|-1 < x < 2\}$. Find the solution set of the inequality $a(x^{2}+1)+b(x-1)+c > 2ax$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \{x|0 < x < 3\} |
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": "345",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Janabel sold two widgets on her first day, and on each succeeding day, she sold three more widgets than she had sold on the previous day. Find the total number of widgets Janabel had sold after working 15 days. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 345 |
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": "356",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In quadrilateral $ABCD,\ BC=10,\ CD=15,\ AD=8,$ and $m\angle A = 90^\circ,\ m\angle B = 60^\circ.$ Given that $AB = r + \sqrt{s},$ where $r$ and $s$ are positive integers, determine $r+s.$ | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 356 |
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": "28",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the sum of all positive divisors of $36$ that are also divisors of $48$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 28 |
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": "n = 1342",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find all natural numbers $n> 1$ for which the following applies:
The sum of the number $n$ and its second largest divisor is $2013$ .
(R. Henner, Vienna) | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | n = 1342 |
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": "180",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If the positive real numbers $x$ and $y$ satisfy $10x+2y+60=xy$, then the minimum value of $xy$ 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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 180 |
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{\\sqrt{2}}{10}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that $$\frac{\tan\alpha}{\tan(\alpha+ \frac{\pi}{4})}$$ = -$$\frac{2}{3}$$, find the value of sin(2$$\alpha$$ + $$\frac{\pi}{4}$$). | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \frac{\sqrt{2}}{10} |
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": "185 \\, \\text{seconds}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The stem-and-leaf plot shows the total duration of one ride on each of the $18$ popular water slides across various water parks. In the stem-and-leaf plot, $3 \ 45$ represents $3$ minutes, $45$ seconds, or $225$ seconds. Determine the median of this dataset, expressed in seconds.
\begin{tabular}{c|ccccc}
1&10&30&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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 185 \, \text{seconds} |
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": "n = 4 \\text{ or } n = 10",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the positive integer values of \( n \) for which \( 2^{n} + 65 \) is a perfect square. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | n = 4 \text{ or } n = 10 |
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": "160\\sqrt{5}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find \[\left|\left(4 + 2i\right)^5\right|\] | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 160\sqrt{5} |
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": "49",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the equation $x + y = 50$, where $x$ and $y$ are positive integers, how many distinct ordered-pair solutions $(x, y)$ exist? | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 49 |
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"
} | Calculate the value of $\sin 37.5^\circ \cos 7.5^\circ - \cos 37.5^\circ \sin 7.5^\circ$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \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": "\\sqrt{10}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given vectors $\overrightarrow{a}=(1,2)$ and $\overrightarrow{b}=(\lambda ,-1)$, if $\overrightarrow{a}$ is perpendicular to $\overrightarrow{b}$, calculate $|\overrightarrow{a}+ \overrightarrow{b}|$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | \sqrt{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": "4097",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $P=\{1,2,3,\ldots ,n\}\left(n\in N,n\geqslant 2\right)$ be a set. Choose two non-empty subsets $A$ and $B$ of $P$ such that the smallest number in $B$ is greater than the largest number in $A$. When $n=10$, the total number of different combinations of $A$ and $B$ is _____. (Please provide your answer as a 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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 4097 |
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": "65^\\circ",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In triangle $PAB$, three tangents to circle $O$ form the sides, and $\angle APB = 50^\circ$. It is given that $\angle BAP = 30^\circ$. Find $\angle AOB$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 65^\circ |
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": "2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What number should be placed in place of \%, so that the following problem has a unique solution: "There are $n$ lines on the plane, intersecting at * points. Find $n$?" | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 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": "3721",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In a school there are \( n \) students, each with a different student number. Each student number is a positive factor of \( 60^{60} \), and the H.C.F. of any two student numbers is not a student number in the school. Find the greatest possible value of \( n \). | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 3721 |
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": "35",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find $x$ if $\log_{10}(3x-5) = 2$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 35 |
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": "38",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Suppose that the roots of $x^3 + 5x^2 + 6x - 8 = 0$ are $p$, $q$, and $r$, and that the roots of another cubic polynomial $x^3 + ux^2 + vx + w = 0$ are $p+q$, $q+r$, and $r+p$. Find $w$. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 38 |
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": "19404",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What is the value of $3^2 \times 4 \times 7^2 \times 11$? | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 19404 |
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\\sqrt{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A regular equilateral triangle with center at the origin in the complex plane has a side length of \( \sqrt{3} \) units. One side of the triangle is parallel to the real axis. Let \( T \) represent the region inside the triangle, and let \( U = \{ z^2 \ | \ z \in T \} \). Find the area of \( U \). | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 3\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": "210x + 90(18 - x) \\geqslant 2100",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Determine the minimum number of minutes the person needs to run to complete a distance of 2.1 kilometers within 18 minutes, given that they walk at a speed of 90 meters per minute and run at a speed of 210 meters per minute. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 210x + 90(18 - x) \geqslant 2100 |
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 a quadratic function $y=ax^2+bx-3$ whose graph passes through points A(2, -3) and B(-1, 0).
(1) Find the expression of the quadratic function;
(2) Fill in the blank: To make the graph of the quadratic function have only one intersection point with the x-axis, the graph should be moved upward along the y-axis 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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 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": "16",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If $g(n)$ is defined as the sum of all the positive divisors of integer $n$, how many integers $j$ exist such that $1 \le j \le 3025$ and $g(j) = 1 + \sqrt{j} + j$? | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 16 |
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"
} | Given $\overrightarrow{m}=(1,1)$, vector $\overrightarrow{n}$ forms an angle of $\frac{3\pi}{4}$ with vector $\overrightarrow{m}$, and $\overrightarrow{m}\cdot\overrightarrow{n}=-1$.
(1) Find vector $\overrightarrow{n}$;
(2) If vector $\overrightarrow{n}$ is perpendicular to vector $\overrightarrow{q}=(1,0)$, and vecto... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 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": "M_1(1, 0), M_2(1, -6)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | On the line \( x = 1 \), find the point \( M \) through which two tangents to the graph of the function \( y = \frac{x^2}{4} \) pass, with the angle between them being \( 45^\circ \). | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | M_1(1, 0), M_2(1, -6) |
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 one of the roots of the equation $3x^2-4x+1=0$ is $a$, then the value of $6a^2-8a+5$ 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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 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": "y(x) = A \\left(1 + x^2 + \\frac{1}{3} x^4 + \\frac{1}{15} x^6 + \\ldots \\right) + B x e^{x^2/2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the solutions of the equation
\[ y^{\prime \prime}-x y-2 y=0 \]
in the form of a power series. | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | y(x) = A \left(1 + x^2 + \frac{1}{3} x^4 + \frac{1}{15} x^6 + \ldots \right) + B x e^{x^2/2} |
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": "O H^2 = 9 R^2 - a^2 - b^2 - c^2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If $A B C$ is a triangle, $O$ is the center of the circumscribed circle with radius $R$, and $H$ is the orthocenter, show the following:
1. $\overrightarrow{O A} \cdot \overrightarrow{O B}=R^{2}-\frac{c^{2}}{2}$;
2. $\overrightarrow{O H}=\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}$;
3. $O H^{2}=9 R^... | [
{
"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{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | O H^2 = 9 R^2 - a^2 - b^2 - c^2 |
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