Having the interface language set to Finnish often causes the assistant to not use web search.
I've been unable to figure out parameters for when this happens, it happens with different models and prompts without a clear explanation.
Even having the custom instructions as "always run a web search, and include links to sources" seems to have no effect, in english nor finnish.
The only way I've found to ensure that the instruction is actually followed, has been to change the interface language to english.
The assistant should run web searches regardless of the interface language, if it determines that the prompt requires sourced information or if specifically instructed to do so.
