You can make external tools available to the LLM and then provide it with instructions for when/how to use them.
So, for example, you'd describe to it that if someone asks it about math or chess, then it should generate JSON text according to a given schema and generate the command text to parametrize a script with it. The script can then e.g. make an API call to Wolfram Alpha or call into Stockfish or whatever.

This isn't going to be 100% reliable. For example, there's a decent chance of the LLM fucking up when generating the relatively big JSON you need for describing the entire state of the chessboard, especially with general-purpose LLMs which are configured to introduce some amount of randomness in their output.

But well, in particular, ChatGPT just won't have the instructions built-in for calling a chess API/program, so for this particular case, it is likely as dumb as auto-complete. It will likely have a math API hooked up, though, so it should be able to calculate a logarithm through such an external tool. Of course, it might still not understand when to use a logarithm, for example.