Recent large language models support inputs of up to 10 million tokens, yet they perform poorly on long-context tasks that require complex reasoning.Such tasks can be solved using only a subset of the input -a proxy contextrather than the full sequence.Despite sharing the same underlying reasoning process, models exhibit a significant performance disparity between proxy and full contexts.To improve long-context reasoning, we propose ProxyCoT, a novel training framework that transfers reasoning capabilities from short proxy contexts to full long contexts.Specifically, we first obtain high-quality chain-of-thought reasoning traces on proxy contexts through reinforcement learning or distillation from a larger teacher model, and then ground the generated traces in full long contexts with supervised fine-tuning.Experiments across different datasets demonstrate that ProxyCoT consistently outperforms strong baselines with reduced computational overhead.Furthermore, models trained with ProxyCoT generalize their long-context reasoning capabilities to out-of-domain tasks. 1