I've been having some trouble with this too. For example, I was generating some fantasy stories with K2 and GLM, using a custom assistant/system prompt, and they're both incorporating phrases like:
By 0200 hours, the temperature had plummeted to forty below zero
On the thirty-eighth day, at 14:23 by his pocket watch, he found them.
I'm pretty sure this is because of the "TIME FORMAT: Hour24" part of Kagi's system prompt which is being tacked onto mine. The less powerful models tend to try to work everything from the prompt into the output whether it makes sense or not.
(This tendency was especially noticeable when location was added to the system prompt a while back.
That was rolled back, but the overall "system prompt misleads LLM" phenomenon is still there.)
I'd prefer if the custom assistant prompt completely overrode the default Kagi system prompt.
Thibaultmol mentioned something in another thread about a "system prompt override" feature: https://kagifeedback.org/d/8793-kagi-assistant-leaks-previous-queries-when-asked-to-use-absolute-mode/3
This might help but I'm not sure how to use it.
Edit: Ahh, checked the Discord, turns out it's "/system_prompt_overwrite" (not override). It goes at the end of the custom assistant prompt. This turns off Kagi's built-in system prompt, solving the problem.