My first thoughts would be to shade the patio area with, an umbrella, shade sail, pergola, or permanent roof structure (cheapest -> expensive) to prevent the concrete from ever getting too hot. Then you're not worrying about coating the concrete with something to reduce the heat, you're treating it at the source by reducing the sun exposure. The three foot perimeter around your pool, I wouldn't worry too much about. It's just like mine and the splashing will take care of the heat there. I'm in Oklahoma and the sun gets really hot, but if there are any number of people out there the perimeter seems to always stay wet and that reduces the heat from the concrete.
I chose to go cheap for my first year and have 2 area rugs on my slightly smaller sized patio space with two 9' octagonal umbrellas. I'm thinking about building a pergola this winter over half that area, but the $50 umbrellas are giving me time to think that through while it's hot without wasting $400 (Self-built pergola price, contracted is much more) and hours of my time. Right now, I like the umbrella option, but it's Oklahoma and the wind only allows me to use them 50% of the time at best.
Maybe someone will chime in on other options like concrete coatings, etc. but I have no knowledge about those other than what I find on Google and here.