Large language models have achieved remarkable progress on complex reasoning tasks. However, they often implicitly fabricate information when inputs are incomplete, producing confident but unreliable conclusions—a failure mode we term ungrounded reasoning. We argue that this issue arises not from insufficient reasoning capability, but from the lack of inferential boundary awareness—the ability to recognize when the necessary premises for valid inference are missing. To address this issue, we propose Grounded Reasoning via Interactive Reinforcement Learning (GRIL), a multi-turn reinforcement learning framework for grounded reasoning under incomplete information. GRIL decomposes the reasoning process into two stages: clarify and pause, which identifies whether the available information is sufficient, and grounded reasoning, which performs task solving once the necessary premises are established. We design stage-specific rewards to penalize hallucinations, enabling models to detect gaps, stop proactively, and resume reasoning after clarification. Experiments on GSM8K-Insufficient and MetaMATH-Insufficient show that GRIL significantly improves premise detection (up to 45%), leading to a 30% increase in task success while reducing average response length by over 20%. Additional analyses confirm robustness to noisy user responses and generalization to out-of-distribution tasks.

Long-form outline generation requires satisfying multiple competing objectives simultaneously: outlines must be engaging, well-organized, topically relevant, and comprehensive while maintaining logical consistency across hierarchical structures. Current approaches either rely on expensive multi-turn interactions with large language models or employ procedural refinement pipelines that cannot systematically learn from critique. We present Logic-RL, a framework that transforms critique-guided outline refinement into a learnable policy through reinforcement learning. Our approach constructs refinement trajectories from teacher demonstrations, synthesizes explicit reasoning chains that decompose the critique-revision process, and optimizes a refinement policy using group relative policy optimization with structure-aware rewards. Experiments on FreshWiki and WikiOutline demonstrate that Logic-RL achieves substantial improvements over strong baselines, with the 0.6B model obtaining 79.17% relative gain and the 1.7B model achieving 8.67% improvement in average rubric scores compared to the best existing methods. Further analysis reveals that learned refinement policies generalize across domains and can be iteratively applied, with quality continuing to improve through three refinement rounds before diminishing returns.