CoT prompting is a technique that allows LLMs to follow a more robust chain of thoughts before giving the final answer to the user. This can lead to better results in some use cases. A common way to do it is instructing the model to use <thinking> tags before producing the "final" answer and ask it to think step-by-step. This is somewhat documented by Claude: https://docs.anthropic.com/en/docs/build-with-claude/prompt-engineering/chain-of-thought
To make the experience better, Kagi could provide an option to hide the thinking process, or to expand it by default. The main problem is that there isn't a standard way to do CoT prompting. Claude seems to have experimented with this through their own web interface. OpenAI's o1 is most likely a model that does the same (and produces more tokens), but OpenAI chooses to completely hide the thinking tokens from the end user, which is not a great approach. In practice, any model can work with CoT prompting, but the bigger models work best with it.
To clarify: it's already possible to make a custom assistant that makes use of this technique. I'm merely suggesting some Assistant UI improvements to make the experience more polished.