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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.