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Despite the remarkable capabilities of large language models, current training paradigms inadvertently foster sycophancy—alignment with user-provided information, regardless of factual accuracy. In this paper, we introduce SMART (Sycophancy Mitigation through Adaptive Reasoning Trajectories), reconceptualizing sycophancy as a reasoning optimization problem rather than an output alignment issue. SMART employs a two-stage approach: (1) Uncertainty-Aware Adaptive Monte Carlo Tree Search (UA-MCTS), which dynamically adjusts exploration based on state-level uncertainty; and (2) progress-based reinforcement learning that distills these improved reasoning patterns into model adaptation. Through extensive experiments, we show that SMART significantly outperforms existing baselines in effectively reducing sycophancy while maintaining performance on out-of-distribution inputs. These findings demonstrate the importance of optimizing internal reasoning processes for developing aligned truthful AI assistant.