Comment by Terr_

I like this mental-model, which rests heavily on the "be careful not to anthropomorphize" approach:

It was already common to use a document extender (LLM) against a hidden document, which resembles a movie or theater play where a character named User is interrogating a character named Bot.

Chain-of-thought switches the movie/script style to film noir, where the [Detective] Bot character has additional content which is not actually "spoken" at the User character. The extra words in the script add a certain kind of metaphorical inertia.