Hello!

I have an 80s steel frame Specialized Allez. It's a 12-speed, and I'm hoping to replace the double cranks on the front with a triple crankset. However, I don't know much about bikes, and I'm not sure how to find out which ones are compatible with my bottom bracket. I've attached a picture, but I'm not sure if it'll help. Also, I'd like more than just the answer of which crankset will be compatible. I want to figure out how to determine that.

Here is the info from the triple crankset I was looking at:
Square taper bottom bracket spindles
172.5mm crank arms
130mm BCD