o1 does not show the reasoning trace at this point. You may be confusing the final answer for the <think></think> reasoning trace in the middle, it's shown pretty clearly on r1.
Reassessing directives
Considering alternatives
Exploring secondary and tertiary aspects
Revising initial thoughts
Confirming factual assertions
Performing math
Wasting electricity
As Karpathy (among others) has noted, the <think> output shows signs of genuine emergent behavior. Presumably the same thing is going on behind the scenes in the OpenAI omni reasoning models, but we have no way of knowing, because they consider revealing the CoT output to be "unsafe."