Agents often repeatedly solve similar task instances from scratch, leading to unnecessary reasoning cost and long execution traces. Prior work has explored workflow reuse and executable skill induction, but it remains unclear which task scenarios admit procedural skills and how the shared procedural structure should be represented across successful traces. We study this problem in FSM-defined scenarios, where successful traces can be viewed as paths in an unknown transition graph, and formulate procedural skills as reusable parameterized control-flow subgraphs. Based on this view, we introduce SkillDisCo, a distillation-and-compilation framework that distills reusable PFSM subgraphs from successful traces and compiles them into callable, executable, and verifiable procedural skills. Experiments on ALFWorld and WebArena show that SkillDisCo improves success rates and reduces agent turns across benchmarks and model scales, demonstrating the benefits of representing shared experience as reusable execution structures.
ReAct-style LLM agents often rediscover the same reasoning routines across problems, yet leave those routines trapped in transient scratchpads. We introduce Reasoning Primitive Induction, a single-pass method that mines successful ReAct traces, clusters recurrent reasoning moves, and converts the most frequent moves into a compact library of typed pseudo-tools. Each pseudo-tool is specified by a natural-language docstring interpreted by an LLM at invocation time, and a standard ReAct loop composes these primitives at test time. The central result is that induced libraries outperform the very agent that generated their traces: by +44pp on RuleArena NBA (30 -> 74), +30pp on MuSR team allocation (38 -> 68), and +22pp on NatPlan meeting planning (7 -> 29). Across five comparable subtasks spanning narrative deduction, rule application, and constraint-satisfaction planning, a single fixed configuration improves over zero-shot Chain-of-Thought on every subtask, matches or surpasses expert-authored decompositions, and outperforms AWM at lower average inference cost.