Long-context inference remains challenging for large language models due to attention dilution and out-of-distribution degradation. Context selection mitigates this limitation by attending to a subset of key-value cache entries, yet most methods allocate a fixed context budget throughout decoding despite highly non-uniform token-level contextual demands. To address this issue, we propose Uncertainty-Triggered Adaptive Context Allocation (UT-ACA), an inference-time framework that dynamically adjusts the context window based on token-wise uncertainty. UT-ACA learns an uncertainty detector that combines semantic embeddings with logit-based confidence while accounting for uncertainty accumulation across decoding steps. When insufficient evidence is indicated, UT-ACA selectively rolls back, expands the context window, and regenerates the token with additional support. Experiments show that UT-ACA substantially reduces average context usage while preserving generation quality in long-context settings. Code and dataset are available at https://github.com/Tommy307/UT-ACA.

Large Language Models (LLMs) often struggle with complex reasoning tasks due to insufficient in-depth insights in their training data, which are frequently absent in publicly available documents. This paper introduces the Chain of Methodologies (CoM), a simple and innovative iterative prompting framework designed to build structured reasoning processes by injecting human methodological insights, thereby enabling LLMs to perform long and effective reasoning for complex tasks. Assuming that LLMs possess certain metacognitive abilities, CoM leverages user-defined methodologies to stimulate the cognitive insights that LLMs have learned implicitly from training data. Experimental results indicate that CoM outperforms competitive baselines, highlighting the potential of training-free prompting methods as general solutions for complex reasoning tasks and the possibility of incorporating human-like methodological insights to bridge the gap to human-level reasoning.