A key aspect is the information bottleneck enforced by the mechanism as the next "iteration" only gets to access the new token computed and discards all the other information it computed.

So if you want it to spend more "time" in a useful manner without changing the architecture, you have to get it to write down the temporary information in the tokens, as "think step by step" does or alternatively iterative prompts "write a draft for the rough structure" "now rewrite it better with more detail".