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[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Let \\( G = (\\mathbb{Z}, +) \\) and \\( H_n \\) be the subgr...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. Using the digits...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Determine the number of odd perfect squares in the set $S = \...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "How does interpreting negative energy electrons as positive e...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. Show that the se...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "In a high-dimensional nonequilibrium system, how can concentr...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Let \\( A \\in M_n(\\mathbb{C}) \\) (\\( n \\geq 2 \\)) be a ...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. Calculate the li...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "In a chess festival with 2017 students, each pair of students...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. The height \\( C...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "In triangle \\( \\triangle ABC \\) with \\( \\angle B = 120^\...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Let \\( O \\) be the center of the circumcircle of \\( \\tria...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. Given a function...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "How does V8's hidden class transition mechanism interact with...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. The product of n...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Let $x_1, x_2, \\ldots, x_7$ be the roots of the polynomial $...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. Find \\( \\cos x...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "What is the relationship between space and the nature of mind...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "If a local educational institution maintains a staffing parad...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. An architect wan...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "How many integers between 1 and 200 are multiples of both 3 a...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "After $k$ balls have been pulled, what's the expected number ...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Find the sum of the coefficients in the polynomial $3(3x^{7} ...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "How does a hybrid MVCC system guarantee serializability under...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Can you propose a C++ program for multiplying two matrices wh...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Find the GCD of 4028 and 6700. Explain the method you use." ...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. On a certain isl...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Solve the equation \\(\\frac{x-2}{2010} + \\sqrt{\\frac{x-3}{...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Evaluate the integral \\(\\iiint\\limits_{V}(2x+y+z)\\,dxdydz...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Compute the remainder when $2^{2007}$ is divided by $1000$." ...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "In quantum thermodynamics, how can one derive a generalized f...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Let \\( X = \\{1, 2, \\ldots, 2018\\} \\) and \\( A \\) be a ...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "What optimization strategies can be employed when compiling h...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "For \\(a > 0\\) and \\(b > 0\\), let \\(r\\) be the radius of...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Determine the value of $a$ such that the number $n = aaaaaa_{...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Given a pentagon $ABCDE$ formed by chords of a circle with si...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "How many ways can 7 books be assigned to 7 reviewers such tha...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "\\nSuppose there is a valve attached to a wheel (tire) as fol...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Let \\( x, y, \\) and \\( z \\) be real numbers such that \\(...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "How many integers $n$ are there such that $n^3 + 8$ has at mo...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Find the nth derivative of the function \\( f(x) = \\frac{1}{...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Consider the set \\( A = \\{4, 9, 16, 25, 36, 49\\} \\). Let ...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "How does the choice of proposal distribution in Metropolis-Ha...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Write a Python 3 script that reads accessibility survey data ...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "In C++20, how can one design a constexpr‑evaluated generic al...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Find all functions \\( f: \\mathbb{Z} \\to \\mathbb{Z} \\) su...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "I was wondering if tension on both ends of a rope is still th...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. Vanya and Petya ...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "How can I optimize a Monte Carlo simulation to speed it up by...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "How many ways can 18 red tokens and 18 blue tokens be placed ...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "For positive numbers \\(a, b, c, x, y, z\\) such that \\(abc ...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. Let $g$ be a lin...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Let \\(S\\) be the number of ordered quintuples \\((a, b, x, ...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Given two string, represented as linked lists (every characte...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "How can strictness analysis be automated to identify thunks c...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. A regular octago...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "If two dice are thrown simultaneously, then find the probabil...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. If \\( 998a + 1 ...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Create an array of 20 unique values from 1 to 50. Write corre...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. In a regular 201...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "How does the observed dispersion measure distribution of fast...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. The first and se...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "In triangle \\(ABC\\), \\(\\angle BAC = 60^\\circ\\), \\(AB =...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. Alice and Bob pl...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Let the triangular area \\(\\Delta = \\{(x, y) \\in \\mathbb{...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Let $E, F, G$ lie on the sides $AB, BC, CA$ of triangle $ABC$...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. In the tetrahedr...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Given \\(a\\), \\(b\\), and \\(c\\) as the sides of a scalene...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Explain how adaptive trace selection in a JIT compiler can ba...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Solve the equation \\((3+\\sqrt{3})^x + (3-\\sqrt{3})^x = (3\...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "What value should the constant $c$ have in order for $x^2 + 1...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "How does Lurie's straightening–unstraightening equivalence ex...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. Prove that if \\...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Find the limit \\(\\lim_{n \\to \\infty} n \\sin(2 \\pi e n!)...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Return your final response within \\boxed{}. In the convex qu...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "A flea is jumping on the vertices of a square $ABCD$. It star...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Can you provide some more information on how to develop a lea...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Add a command to change the representation of the molecules" ...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Write a Python function that extracts audio features from a ....
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Compute the integral $\\int_0^\\infty\\frac{\\arctan x}{x^2+2...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Let \\( Q \\) be the first Fibonacci number with six differen...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Generate an executable Python function generated from the giv...
[ { "role": "system", "content": "You are a highly capable AI assistant. For every response, you must first show your step-by-step reasoning process within a <think> block, followed by the final answer." }, { "role": "user", "content": "Evaluate the limit \\(\\lim_{a \\to 0} \\int_0^a \\frac{1}{\\...