Which brain networks do these actions involve?

Well, if you realize – that is, you really “know” – that the brain controls all of our bodies’ functions, at least in terms of sending the signals to the muscles to contract or relax to permit movement, then it should be pretty obvious.

Do you have to think about your breathing, the motions that it takes to get up out of a chair and to walk across a room? I’m not saying that you can’t think of those things, but do you need to? That’s generally controlled by a part of the brain that takes charge of “default” actions that you can do without thinking. (To the extent that you practice more and more things: throwing a ball, running fast and then “as fast as you can for as long as you can”, and so forth, you can become more skilled at more things on a “muscle memory” basis. It’s not really “muscle memory”; your brain still needs to control all of the functions, but you may not have to think so much.)

On the other hand, if your intent is to plan an invasion, a robbery or the rules to organize civilization, then you probably can’t do that without thinking. A lot.

I haven’t given names to the parts of the brain responsible for the differentiation between these kinds of tasks, but if you have the names, then here is a way (I’m not saying that it’s the only way, either) to differentiate. There are also autonomous functions that don’t involve the body actually moving, or which involve “automatic” reactions to stimuli such as loss of balance, reactions to heat and cold and smells, etc., and that also involve the brain.

The human brain is like an enormous fish—it is
flat and slimy and has gills through which it can see.
—Monty Python