In document AI, reliable analytics require converting long, noisy (often multi-document) corpora into heterogeneous structured data—e.g., tables for numerical fields, graphs for relations, and trees for hierarchies. Yet, one-pass LLM extraction often yields incomplete or inconsistent structures because it lacks explicit verification and opportunities to revise earlier choices. We present CycleIE, an iterative information extraction (IE) framework that closes the loop between reasoning and acting by coupling ReAct with Monte Carlo Tree Search (MCTS). CycleIE employs a multi-agent workflow to iteratively retrieve, structure, extract, and refine content under verification guidance. By treating extraction as a feedback-driven search process, CycleIE systematically corrects omissions and inconsistencies that defeat one-pass methods, while remaining orthogonal to retrieval-augmented generation (RAG). Experiments on challenging document-based QA benchmarks demonstrate that CycleIE delivers >10% relative improvements over strong baselines, particularly in lengthy or multi-document contexts.