Earlier quoted context omitted.
I think this problem needs to be solved at a higher level, and in fact Bard is doing exactly that. The model itself generates its output, and then higher-level systems can fact check it. I've heard promising things about feeding back answers to the model itself to check for consistency and stuff, but that should be a higher level function (and seems important to avoid infinite recursion or massive complexity stemming…
I'm not a fan of current approaches here. "Chain of thought" or other approaches where the model does all its thinking using a literal internal monologue in text seem like a dead end. Humans do most of their thinking non-verbally and we need to figure out how to get these models to think non-verbally too. Unfortunately it seems that Gemini represents no progress in this direction.
Insofar as we can say that models think at all between the input and the stream of tokens output, they do it nonverbally. Forcing the structure of reduce some of it to verbal form short of the actual response-of-concern does not change that, just as the fact that humans reduce some of their thought to verbal form to work through problems doesn't change that human thought is mostly nonverbal.
(And if you don't consider what goes on between input and output thought, than chain of thought doesn't force all LLM thought to be verbal, because only the part that comes out in words is "thought" to start with in that case -- you are then saying that the basic architecture, not chain of thought prompting, forces all thought to be verbal.)