Chain-of-thought prompting improves reasoning by generating intermediate steps as discrete text, but each step is forced to commit to a single token even when the model is uncertain. Continuous latent reasoning offers an alternative: a latent state can preserve multiple candidate interpretations without immediately selecting one token. Existing training-free approaches either place latent states only before decoding or switch between explicit and latent modes without optimizing the inserted state itself. We propose MidThink, a training-free framework that inserts and optimizes latent blocks both at the start of reasoning and adaptively during generation. When a confidence trigger detects sustained mid-stream uncertainty, MidThink inserts a new latent block and refines it with a rollout-based reward computed from short future continuations. We further show that initialization strongly affects whether a mid-stream block preserves a superposition over multiple tokens or collapses toward a single token. Across five mathematical reasoning benchmarks, MidThink improves over training-free latent-reasoning baselines, with the largest gains on the AIME benchmarks. Mechanistic analysis links these gains to three measurable properties of the latent block: distributional entropy across layers, attention centroid position, and stability under reinforcement learning updates.

Step-by-step reasoning has become a standard approach for large language models (LLMs) to tackle complex tasks. While this paradigm has proven effective, it raises a fundamental question: How can we verify that an LLM’s reasoning is accurately grounded in knowledge? To address this question, we introduce a novel evaluation suite that systematically assesses the knowledge grounding of intermediate reasoning. Our framework comprises three key components. (1) Principal Knowledge Collection, a large-scale repository of atomic knowledge essential for reasoning. Based on the collection, we propose (2) knowledge-grounded evaluation metrics designed to measure how well models recall and apply prerequisite knowledge in reasoning. These metrics are computed by our (3) evaluator LLM, a lightweight model optimized for cost-effective and reliable metric computation. Our evaluation suite demonstrates remarkable effectiveness in identifying missing or misapplied knowledge elements, providing crucial insights for uncovering fundamental reasoning deficiencies in LLMs. Beyond evaluation, we demonstrate how these metrics can be integrated into preference optimization, showcasing further applications of knowledge-grounded evaluation. Our evaluation suite is publicly available.