How Large Reasoning Models Solve Problems: A Mechanistic Study on Tower of Hanoi

Large reasoning models (LRMs) have exhibited strong reasoning abilities widely attributed to deliberate thinking through long internal chains of thought (CoT). However, there has been significant debate about whether the content of CoT traces is causally relevant for the performance of these models. In this paper, we conduct a mechanistic study of CoT traces on a task adapted from the classic Tower of Hanoi puzzle to understand how open-source LRMs solve problems. We selected gpt-oss 20b and gpt-oss 120b, both of which achieve around 95\% accuracy on the task under high reasoning effort. We identified 6 dominant reasoning patterns deployed for finding solutions, including analogy identification, human-like strategic problem solving, and systematic search. Focusing on strategic problem solving episodes, we identified self-verification as an important reasoning primitive guiding the outcome of these episodes. By intervening on the verification process — either correcting verification errors or corrupting correct verifications — we established a causal link between these self-verification behaviors and the accuracy of the final solution. Using causal mediation analysis, we further identified a sparse set of experts in the Mixture-of-Experts layers with strong causal effects on verification behavior, and showed that the outputs of these experts can be aggregated to induce verification behavior. Together, these experiments provide causal evidence that the content of CoT traces, and self-verification behaviors in particular, meaningfully shape the final answers generated by LRMs, and begin to uncover the internal mechanisms that support these capacities.