Sequential reasoning in agent systems has been significantly advanced by large language models (LLMs), yet existing approaches face limitations. Reflection-driven reasoning relies solely on knowledge in pretrained models, limiting performance in novel scenarios, while experience-assisted reasoning often depends on external experiences and lacks clear principles for selecting representative experiences. We address these limitations by proposing CoPS (Cross-Task Experience Sharing), a generalizable algorithm that enhances sequential reasoning by cross-task experience sharing and selection. In detail, CoPS leverages agents' experiences on previous tasks, selecting distribution-matched experiences via a provable pessimism-based strategy to maximize utility while minimizing risks from distribution shifts. Extensive experimental results on benchmarks like Alfworld, Webshop, and HotPotQA demonstrate that CoPS consistently outperforms state-of-the-art baselines, with superior sample efficiency suitable for resource-constrained scenarios. Theoretically, we show that the performance of our algorithm depends on both the quality of the pretrained LLM and the matching between the agent's task-dependent trial distribution and that generated by the LLM. Our work bridges the gap between existing sequential reasoning paradigms and validates the effectiveness of leveraging cross-task experiences, shedding light on the potential to improve agents' generalization and adaptability across diverse tasks. Our codes are available at $\href{https://github.com/uclaml/COPS}{\text{https://github.com/uclaml/COPS}}$.