{"task": {"agent_timeout": 3000, "task": "aime_ii-13", "verifier_timeout": 3000, "instruction": "  Solve the following problem. Reason step by step, create the file `/app/answer.txt`, and put your final answer there.\n  Your answer should be a single integer from 1 to 999 inclusive.\n\n    Let $x_1, x_2, x_3, \\ldots$ be a sequence of rational numbers defined by $x_1 = \\frac{25}{11}$ and\n  $$x_{k+1} = \\frac{1}{3}\\left(x_k + \\frac{1}{x_k} - 1\\right)$$\n  for all $k \\ge 1$. Then $x_{2025}$ can be expressed as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find the remainder when $m + n$ is divided by $1000$.\n", "memory": "", "runnable": false, "difficulty": "unknown", "language": "", "cpus": "", "instruction_truncated": false, "category": "reasoning", "compose": false, "has_solution": true, "oracle": null, "docker_image": "", "taskset": "aime", "tags": ["math", "AIME"]}, "runs": []}