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.

Recurrent neural network-based sequence-to-sequence (S2S) models have been extensively applied for multistep-ahead time-series forecasting. These models typically involve a decoder trained using either its previous forecasts or the actual observed values as the decoder inputs. However, relying on self-generated predictions can lead to the rapid accumulation of errors over multiple steps, while using the actual observations introduces exposure bias as these values are unavailable during the inference stage. In this regard, this study proposes a novel training approach called reinforced decoder, which introduces auxiliary models to generate alternative decoder inputs that remain accessible when extrapolating. In addition, a reinforcement learning algorithm is utilized to dynamically select the optimal inputs to improve accuracy. Comprehensive experiments demonstrate that our approach outperforms representative training methods over several datasets. Compared to the best baseline, the proposed method based on long short-term memory yields average relative improvements of 5.98% in root mean square error, 4.39% in mean absolute percentage error, and 7.63% in$\text{R}^{2}$. Furthermore, the proposed approach can also achieve promising performance when generalized to Transformer-based S2S forecasting models.