First of all, this is not the generic 'make me a better programmer' question, even though the outcome of asking this question might seem similar to it. On programmers.SE, I've read and seen these get closed here, here, here, here, and here.
We all know there are a multitude of generic suggestions to hone your programming skills (e.g reading SO, reading recommended books, following blogs, getting involved in open-source projects, etc.). This is not what I'm after.
I also acknowledge the active readership on this web site and am hoping it works in my favour by yielding some great answers. From reading correspondence here, there appears to be a vast number of experienced people who are working, or have worked, programming-related fields. And most of you can convey thoughts in an eloquent, concise manner.
I've recently noticed the distinction between someone who's capable of programming and a programmer who can really think. I refuse to believe that in order to become great at programmer, we simply submit ourselves to a lifetime of sponge-like behaviour (i.e absorb everything related to our field by reading, listening, watching, etc.). I would even state that simply knowing every single programming concept that allows you to solve problem X faster than everyone around you, if you can't think, you're enormously limiting yourself - you're just a fast robot.
I like to believe there's a whole other face of being a great programmer which is unrelated to how much you know about programming, but it is how well you can intertwine new concepts and apply them to your programming profession or hobby. I haven't seen anyone delve into, or address, this facet of the human mind and programming. (Yes, it's also possible that I haven't looked hard enough too - sorry if that's the case.)
So for anyone who has spent any time thinking about what I've mentioned above - or maybe it's everyone here because I'm a little behind in my personal/professional development - what are your suggestions on learning how to think? Aside from the usual reading, what else have you done to be better than the other people in your/our field?