Not trying to be cynical here, but I am genuinely interested is there a reason why these LLM don't/can't/won't apply some deterministic algorithm? I mean, counting characters and such, we have solved those problems ages ago.
They are stuck in a place where the models are expected to do two things simultaneously. People want them to show the peak of pure AI ability while at the same time be the most useful they can be.
Err too much on the side automatic use of tools and people will claim you're just faking it, fail to use tools sufficiently and people will claim that the AI is incapable of operations that any regular algorithm could do.
The old human vs animal differentiator was humans build and use tools.
If you allow ChatGPT to use its memory feature (I deliberately turn that off) and ask those kinds of questions enough it might even make a note about this itself.