Reasoning-augmented recommender systems (RecSys) enhance user preference modeling by generating reasoning trajectories over historical interactions before making recommendations. Knowledge distillation provides a practical paradigm for transferring such reasoning capabilities from powerful large language models to lightweight RecSys. However, existing methods typically rely on a single fixed teacher, remain constrained by the teacher knowledge ceiling, and indiscriminately distill teacher-generated trajectories without assessing their actual utility for downstream recommendation. To address these limitations, we propose MUSE (Multi-Teacher Utility-guided Selection with Self-Exploration), an adaptive reasoning distillation framework that jointly improves reasoning generation and reasoning utilization. MUSE first constructs a diverse reasoning pool using multiple teacher LLMs and progressively augments it via student self-exploration, enabling the student to leverage the strengths of different teachers and gradually explore reasoning strategies beyond teacher imitation. We then develop Rank-Gain Utility Assessment (RGUA), which evaluates each candidate according to the normalized full-catalog rank improvement of the ground-truth item and identifies the most and least recommendation-beneficial trajectories. Based on these utility-aware trajectory pairs, we introduce dual-level contrastive learning objectives that guide the student generator to prefer beneficial reasoning while training the recommendation encoder to more effectively exploit recommendation-relevant preference evidence. Extensive experiments on three real-world datasets demonstrate the effectiveness and robustness of the proposed framework.

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