Large multimodal reasoning models solve challenging visual problems via explicit long-chain inference: they gather visual clues from images and decode clues into textual tokens. Yet this capability also increases hallucinations, where the model generates content that is not supported by the input image or the question. To understand this failure mode, we identify \emph{reasoning drift}: during clue gathering, the model over-focuses on question-irrelevant entities, diluting focus on task-relevant cues and gradually decoupling the reasoning trace from visual grounding. As a consequence, many inference-time localization or intervention methods developed for non-reasoning models fail to pinpoint the true clues in reasoning settings. Motivated by these insights, we introduce ClueRecall, a metric for assessing visual clue retrieval, and present ClueTracer, a training-free, parameter-free, and architecture-agnostic plugin for hallucination suppression. ClueTracer starts from the question and traces how key clues propagate along the model's reasoning pathway (question $\rightarrow$ outputs $\rightarrow$ visual tokens), thereby localizing task-relevant patches while suppressing spurious attention to irrelevant regions. Remarkably, \textbf{without any additional training}, ClueTracer improves all \textbf{reasoning} architectures (including \texttt{R1-OneVision}, \texttt{Ocean-R1}, \texttt{MM-Eureka}, \emph{etc}.) by $\mathbf{1.21\times}$ on reasoning benchmarks. When transferred to \textbf{non-reasoning} settings, it yields a $\mathbf{1.14\times}$ gain.