Understanding human intentions in videos requires deep cognitive reasoning, yet Multimodal Large Language Models (MLLMs) frequently suffer from factual hallucinations and counterfactual blindness. To address these limitations, we introduce ASTRO, a novel framework that navigates Intention Reansoning Tree to guide preference optimization. Our approach employs a collaborative multi-agent system integrated with Monte Carlo Tree Search (MCTS) to systematically explore complex reasoning spaces based on visual evidence. By navigating this tree, ASTRO dynamically extracts distinct cognitive trajectories—correct, error, and ambiguous paths—to construct high-quality preference pairs. Finally, we apply Direct Preference Optimization (DPO) using these contrastive paths, explicitly enhancing the model’s factual grounding and sensitivity to causal boundaries. Extensive experiments across complex video intention benchmarks demonstrate that ASTRO achieves superior performance while exhibiting remarkable data efficiency, significantly outperforming fully supervised baselines using only a fraction of the original training data.