Actually, anthropomorphizing a bit, if I take something I vaguely remember how to do, say integration by parts, then if I turn off my own brain's "reasoning", then the "skill" I would generate would almost certainly be wrong, and no help in solving a problem. But if I turn reasoning on, I'd probably be able to come up with the correct algorithm and write it as a skill, sure, but if reasoning is on, I'd be able to solve the problem without needing to write down the algorithm itself (and might even be more successful that way, with something concrete to work with).

OTOH something I know innately how to do, like long division, writing down the algorithm doesn't help at all. In fact if someone just gave me that algorithm and for whatever reason I didn't recognize what it was, I'd have a lot harder time following the instructions than just innately dividing the numbers.

If course anthropomorphizing is always dangerous, but it does provide potential reasons why my above rationale could be wrong.