The main point I was trying to make is that adding the prompt "think carefully" moves the model toward the "riddle" vector space, which means it will draw tokens from there instead of the original space.

And I doubt there are any such hidden capabilities because if there were it would be valuable to OpenAI to surface them (e.g. by adding "think carefully" to the default/system prompt). Since adding "think carefully" changes the output significantly, it's safe to assume this is not part of the default prompt. Perhaps because adding it is not helpful to average queries.