CNA or nursing pre-reqs?

I am hoping to go to nursing school in the next few years. My question is shoul I become trained as a CNA to get some patient care experience or should I start taking some of the pre-requisites for nursing school? I do not currently have any patient care experience. I will need to take Chemistry, Algebra, etc. before I can be accepted into nursing school.
I'd go for the pre-reqs if you have to pick but why not do both? Many programs don't even make you have patient care experience although it can be helpful.