Large Language Models (LLMs) frequently generate buggy code with complex logic errors that are challenging to diagnose. While existing LLM-based self-repair approaches conduct intensive static semantic analysis or reply on superficial execution logs, they miss the in-depth runtime behaviors that often expose bug root causes-lacking the interactive dynamic analysis capabilities that make human debugging effective. We present InspectCoder, the first agentic program repair system that empowers LLMs to actively conduct dynamic analysis via interactive debugger control. Our dual-agent framework enables strategic breakpoint placement, targeted state inspection, and incremental runtime experimentation within stateful debugger sessions. Unlike existing methods that follow fixed log collection procedures, InspectCoder adaptively inspects and perturbs relevant intermediate states at runtime, and leverages immediate process rewards from debugger feedback to guide multi-step reasoning, transforming LLM debugging paradigm from blind trial-and-error into systematic root cause diagnosis. We conduct comprehensive experiments on two challenging self-repair benchmarks: BigCodeBench-R and LiveCodeBench-R. InspectCoder achieves 5.10%-60.37% relative improvements in repair accuracy over the strongest baseline, while delivering 1.67x-2.24x superior bug-fix efficiency respectively. We also contribute InspectWare, an open-source middleware that abstracts debugger complexities and maintains stateful debugging sessions across mainstream Python testing frameworks. Our work provides actionable insight into the interactive LLM-debugger systems, demonstrating the significant potential of LLM-driven dynamic analysis for automated software engineering.

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