The field of large language models (LLMs) is rapidly evolving, with a focus on enhancing their reasoning and problem-solving capabilities. Recent developments indicate a shift towards improving the reliability and faithfulness of LLMs in high-stakes fields such as medicine, where accuracy and comprehensiveness are crucial. Notable progress has been made in addressing the 'Structure Gap' between the probabilistic nature of token generation and the deterministic requirements of structured data formats. This has led to the development of innovative reinforcement learning frameworks that can efficiently enforce strict syntactic constraints, reducing inference latency and improving overall performance. Furthermore, there is a growing interest in analyzing and improving LLM reasoning through novel representations and metrics. These advancements enable a deeper understanding of the underlying reasoning processes and facilitate the development of more effective and efficient methods for training LLMs. The use of multi-objective reinforcement learning methods, verifiable reward signals, and instruction-policy co-evolution frameworks are also being explored to align LLM reasoning with specific objectives and improve their overall performance. Some papers are particularly noteworthy for their innovative approaches, such as the introduction of ReJump, a tree-jump representation for analyzing and improving LLM reasoning, and the development of AutoBRANE, an efficient algorithm for learning branching networks in multitask algorithmic reasoning. Additionally, the proposal of UnsolvableQA and UnsolvableRL for detecting unsolvable problems and the introduction of ThinkMerge, a plug-and-play decoding strategy for open-ended reasoning, demonstrate the diversity of research in this area.