It only "knows" what it writes down and if you force it to print the intermediate step it can more accurately get to the final answer.
These models do not "think". This is a fundamental misunderstanding of how they work. It's not AI. It's not even language. It's just text inference.
So it's still fair to say you can ask it to think
I would suggest that a person saying "ask the model to think about" in this context in no way implies that that person is confused about the nature of the model, it is simply a convenient piece of language that helps us to achieve the desired result.
Yes, it does. Assuming GPT "thinks" is shaping public perception and that's already gone much too far.
It looks you just pattern-matched on the word _think_ and replied with a pre-made opinion about how AIs can't think. Ironic...