The recent developments in the research area of program synthesis and verification, particularly leveraging Large Language Models (LLMs), indicate a significant shift towards more automated and integrated solutions. The field is moving towards enhancing the reliability and efficiency of code generation and verification processes by embedding advanced control mechanisms within LLMs. This includes the integration of neural networks with feedback control, multi-agent systems for verification, and the direct embedding of control logic within language model prompts. These innovations aim to bridge the gap between adaptive reasoning capabilities of LLMs and structured control mechanisms of traditional software paradigms. Notably, there is a growing focus on ensuring correctness and safety in code generation, especially in critical domains like industrial control systems and motion control. The advancements are not only improving accuracy and reducing operational costs but also paving the way for more scalable and extensible verification frameworks. Additionally, there is a trend towards formalizing and automating proof generation for code, which is crucial for maintaining high standards of correctness in software development. Overall, the field is evolving towards more sophisticated, automated, and reliable systems that can handle complex tasks with higher precision and safety.