Human-AI planning for complex goals remains challenging with current large language models (LLMs), which rely on linear chat histories and simplistic memory mechanisms. Despite advances in long-context prompting, users still manually manage information, leading to a high cognitive burden. Hence, we propose JumpStarter, a system that enables LLMs to collaborate with humans on complex goals by dynamically decomposing tasks to help users manage context. We specifically introduce task-structured context curation, a novel framework that breaks down a user's goal into a hierarchy of actionable subtasks, and scopes context to localized decision points, enabling finer-grained personalization and reuse. The framework is realized through three core mechanisms: context elicitation, selection, and reuse. We demonstrate that task-structured context curation significantly improves plan quality by 16% over ablations. Our user study shows that JumpStarter helped users generate plans with 79% higher quality compared to ChatGPT.