Right, to express it another way: The real-world LLM just makes documents longer. It is being run against a document which resembles a movie script, where "User says X, Computer says" is inserted whenever I type X, and then the LLM just makes it a bit longer to complete the line for the "Computer" character.

These models marketed as "reasoning" are just changing the style of the script to film noir detective, where the protagonist "Computer" has extra observations and commentary that aren't "spoken" to other characters.

While that change may help keep the story on track, it does not affect the fundamental nature of the "thinking" going on: It's still just growing a document and acting out whatever story emerges.