{"task": {"agent_timeout": 600, "task": "omnimath_2517", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nLet \\(ABC\\) be a triangle with \\(AB=8, AC=12\\), and \\(BC=5\\). Let \\(M\\) be the second intersection of the internal angle bisector of \\(\\angle BAC\\) with the circumcircle of \\(ABC\\). Let \\(\\omega\\) be the circle centered at \\(M\\) tangent to \\(AB\\) and \\(AC\\). The tangents to \\(\\omega\\) from \\(B\\) and \\(C\\), other than \\(AB\\) and \\(AC\\) respectively, intersect at a point \\(D\\). Compute \\(AD\\).\n\n## Instructions\n\nSolve the mathematical problem above and write your final answer to `/workspace/answer.txt`.\n\n**Important**: Write only your final answer to the file, not the full solution process.\n\n### Guidelines\n\n- Provide your final numerical answer or mathematical expression\n- Write the answer as plain text (no special formatting needed)\n- Be precise and clear in your answer\n- The answer should directly respond to what the problem asks for\n\n### Example\n\nIf the problem asks \"What is 2 + 2?\", your answer file should contain:\n\n```\n4\n```\n\nYour answer will be evaluated against the correct solution using an automated grading system.\n", "memory": "", "runnable": false, "difficulty": "hard", "language": "", "cpus": "", "instruction_truncated": false, "category": "math", "compose": false, "has_solution": true, "oracle": null, "docker_image": "", "taskset": "omnimath", "tags": ["omni-math"]}, "runs": []}