Growing evidence suggests that large language models do not use their depth uniformly, yet we still lack a fine-grained understanding of their layer-wise prediction dynamics. In this paper, we trace the intermediate representations of several open-weight models during inference and reveal a structured and nuanced use of depth. Specifically, we propose a "Guess-then-Refine" framework that explains how LLMs internally structure their computations to make predictions. We first show that the top-ranked predictions in early LLM layers are composed primarily of high-frequency tokens, which act as statistical guesses proposed by the model due to the lack of contextual information. As contextual information develops deeper into the model, these initial guesses get refined into contextually appropriate tokens. We then examine the dynamic usage of layer depth through three case studies. (i) Multiple-choice task analysis shows that the model identifies appropriate options within the first half of the model and finalizes the response in the latter half. (ii) Fact recall task analysis shows that in a multi-token answer, the first token requires more computational depth than the rest. (iii) Part-of-speech analysis shows that function words are, on average, the earliest to be predicted correctly. To validate our results, we supplement probe-based analyses with causal manipulations in the form of activation patching and early-exiting experiments. Together, our results provide a detailed view of depth usage in LLMs, shedding light on the layer-by-layer computations that underlie successful predictions and providing insights for future works to improve computational efficiency in transformer-based models.