Models employing long chain-of-thought (CoT) reasoning have shown superior performance on complex reasoning tasks. Yet, this capability introduces a critical and often overlooked inefficiency -- overthinking -- models often engage in unnecessarily extensive reasoning even for simple queries, incurring significant computations without accuracy improvements. While prior work has explored solutions to mitigate overthinking, a fundamental gap remains in our understanding of its underlying causes. Most existing analyses are limited to superficial, profiling-based observations, failing to delve into LLMs' inner workings. This study introduces a systematic, fine-grained analyzer of LLMs' thought process to bridge the gap, TRACE. We first benchmark the overthinking issue, confirming that long-thinking models are five to twenty times slower on simple tasks with no substantial gains. We then use TRACE to first decompose the thought process into minimally complete sub-thoughts. Next, by inferring discourse relationships among sub-thoughts, we construct granular thought progression graphs and subsequently identify common thinking patterns for topically similar queries. Our analysis reveals two major patterns for open-weight thinking models -- Explorer and Late Landing. This finding provides evidence that over-verification and over-exploration are the primary drivers of overthinking in LLMs. Grounded in thought structures, we propose a utility-based definition of overthinking, which moves beyond length-based metrics. This revised definition offers a more insightful understanding of LLMs' thought progression, as well as practical guidelines for principled overthinking management.