I think when they advertise "thinking" it just does a few more iterations of giving you the closest "number in your head from the clues you've given it (requirements).
I saw someone once say that LLMs are a kind of "word calculator" and I feel that's quite a good description.
A simple example:
Prompt:Make it yellow
Think: the user wants something yellow but hasn't said what it is. Previously the user talked about creating a Button, so it must be the button but I should clarify by asking
Response: is it the button that you want yellow?
All of the recent improvements in the LLM's "thinking" have just been layers of programming on top of its statistical models. Which is why its becoming clear LLMs are really not advancing that much.