What to Ask Next? Probing the Imaginative Reasoning of LLMs with TurtleSoup Puzzles

We investigate the capacity of Large Language Models (LLMs) for imaginative reasoning—the proactive construction, testing, and revision of hypotheses in information-sparse environments. Existing benchmarks, often static or focused on social deduction, fail to capture the dynamic, exploratory nature of this reasoning process. To address this gap, we introduce a comprehensive research framework based on the classic "Turtle Soup" game, integrating a benchmark, an agent, and an evaluation protocol. We present TurtleSoup-Bench, the first large-scale, bilingual, interactive benchmark for imaginative reasoning, comprising 800 turtle soup stories sourced from both the Internet and expert authors. We also propose Mosaic-Agent, a novel agent designed to assess LLMs' performance in this setting. To evaluate reasoning quality, we develop a multi-dimensional protocol measuring logical consistency, detail completion, and conclusion alignment. Experiments with leading LLMs reveal clear capability limits, common failure patterns, and a significant performance gap compared to humans. Our work offers new insights into LLMs' imaginative reasoning and establishes a foundation for future research on exploratory agent behavior.