> Sentences that orbit a point, then jump to it like it's a revealed insight.

Is this inside the thinking tokens, or the output?

As this type of stuff is expected for thinking, because of the whole CoT / “think step by step” works, as this is optimal for the way LLMs work with attention and next word prediction.

So the fact that it first “orbits” a point only to get to the conclusion afterwards is the system working as designed.

Eg “what is 3 * 3 + 5?”

without CoT, it would just just answer “8” for example.

with CoT, it would answer something like “<thinking>I need to think step by step. 3 * 3 + 5 can be rewritten as “(3 * 3) + 5”. I first need to calculate 3 * 3 = 9. Now I need to calculate 9 + 5 = 14. That was the last calculation. The final answer is 14.

I now need to give the user the final answer. </thinking>.

14“

Etc.

You forgot about 1000 lines of "<thinking>Wait, but different idea here</thinking>" ;)

It's the output.