In your floor-sweeping example, I agree that you cannot scale previous solutions to 10^25. And I agree that you need very novel thoughts to solve that larger problem, that involve the ability to come up with new ideas and build things from them.

Could you give a concrete example of how 'rationality skills' fits into that picture, and point at a mechanism by which getting better at these skills causes you to be able to solve the 10^25 level problem?