Thinking, analyzing, playing? I think it depends on the player or person and what "spectrum" you might exist or think in.
I'm a bit of a musician, and in my career I have met and been associated with some people that just could. Incredible ear, incredible talent, they just sat at the piano and they could, for whatever reason they're at home at the keyboard, they look at it and it just makes sense, they don't think, they don't analyze, they just listen, then they just play. For others it took hours of lessons and countless hours of practice. For the lesson takers though, after all that hard work, maybe they became the complete package, they know their craft inside and out, and for the most part the players could just play and for a lot of them that was enough. They didn't want to be bothered with the science or application, they just wanted to play, and boy, could they ever play.
I think pool is very much the same, some people just can, then there are those of us that really need to work at it. The table doesn't make the same sense to me that the keyboard does, I look at the table and I have to think. I break the balls and I have to look for a minute and consider and develop a plan. I play with some guys, they break and 30 seconds later they're on a straight in 9 ball shot. Pool is just their thing.
Pool and analysis - some people need to, others just can. I think playing smart is a widely underdeveloped skill.
As I reduce the number of steps that I take to make a shot and get shape my level of playing ability is approaching theirs, but I'll likely never be at their level of talent when it comes to pool.
It's becoming more reactive for me and I'm becoming a better shotmaker. If the balls weren't round there would be far fewer variables so I am hopeful that I never give up on thinking. I have found that can be, at times, an advantage.