You pointed to something that was out of date. I helped you make your argument stronger and you got butthurt about it.

Glad I could teach you something, kid.

Your first one is actually a pretty good example of something a lot of LLM fanatics won't believe. They believe in "reasoning" models as actually reasoning, and are not receptive to the reality that while it looks like reasoning, and even obviously the expenditure of more tokens is resulting in better final results, it isn't "reasoning".

It declares step 3 to be 'botched' and then does the exact same step 3 and declares it good, and from an actual reasoning perspective it makes no sense, as it would have been step 4 that was about to be a mistake.

So it arrives at the correct sequence, but it clearly didn't get through by "logic-ing" it, it just modeled that a mistake should be acknowledged around step three, because that's when folks generally flub it, and presented the rationale that is always provided to explain. It doesn't make actual sense, but it has the effect of the correct answer being reached, but not through actual abstract reasoning.