Large language model (LLM) agents acting across web applications and online services often need multi-turn corrections to align their work with users' underspecified goals and preferences. In practice, users may identify problems in the current outcome without specifying the desired result, so learning user intentions requires interpreting each correction against the agent's preceding and revised outcomes. These expectations are often connected to a particular context, making it hard to know when they apply and how to ensure the agent later acts as the user expects. To this end, we propose LiveAsset, an intent harness that learns reusable intent assets from corrective interactions and uses them for runtime control of agent execution. LiveAsset jointly interprets each correction with the agent's original and revised results to infer user intent, incrementally updating the assets while preserving earlier requirements that remain applicable. The learned requirements guide agent execution from task entry and provide criteria for runtime verification, which uses the explanations to assess applicability before each reply is delivered and directs the agent to revise the result to address unmet requirements while preserving those already satisfied. Following a learning phase in which simulated users progressively reveal requirements through multi-turn corrections, we evaluate LiveAsset using same-task replay of the original requests on π-Bench, PERMA, and Vita and cross-task transfer on PAST-Bench and SkillEvolBench. Experiments show that LiveAsset better fulfills requirements learned from corrective interactions and improves performance on these benchmarks compared with memory, skill, and rule-based harness baselines. Code is available at github.com/landian60/LiveAsset.

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