Based on my previous attempts with that other well noted LLM, I don't think these models are at all good at managing "theory of mind". They seem to not keep track very well of which parties are privy to which information, which parties are supposed to be pursuing certain conversational objectives, and generally which direction information is supposed to be flowing. It often trips over itself at the level of 2 parties…
They are an example of a situation where putting excess effort into a problem returns a plausible result, but from an efficiency and accuracy standpoint, parts of what they are accomplishing are better solved by simpler systems.
As they act as an interpreter, they should be able to identify when to hand off tasks to subroutines, and then reincorporate the result.
Just because LLMs can successfully output what they are doing, doesn't mean they are the best tool for the job. They are sort of like a CPU, good at generalist everything tasks, better when augmented with coprocessors.