Add Per-Instance Program Synthesis module and tests #9036
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This adds Per-Instance Program Synthesis (PIPS) from the NeurIPS '25 paper Once Upon an Input: Reasoning via Per-Instance Program Synthesis (https://openreview.net/forum?id=XsQNqRdcdh).
PIPS is an agent which solves problems by either using code generation and execution or Chain of Thought, choosing the reasoning mode by having the model select on a per-instance basis. When code execution is chosen, the final answer is computed entirely via code from an abstracted version of the input. PIPS also refines the generated code based on feedback from another LLM process which critiques the code. This refinement process is vital since frontier models tend to hardcode (wrong) answers within code rather than use the code to actually compute anything. On many reasoning benchmarks, PIPS significantly outperforms Chain of Thought, Program of Thought, and CodeAct.