Hello Robson, my name is John, nice to meet you. If you're going to use "for" then you have to use a gerund after it. For example: "Think about the reasons for exercising." Now if you're going to use "to" then this makes it a "to-infinitive" so then you would use the base verb "exercise". For example: "Think about the reasons to exercise." Both are correct and natural. You just have to figure out how you want to say it. I hope this helps.

It is better to use exercise as a verb here, so 'to exercise' is correct.

I was thinking the same. But if go to 'youenglish.com' and look for "for excercise" you find tons of prhases like that: .. So, the way to do it, it's very important to have facilities on a campus for exercise,... in this context, Could It be understood as "the activity" The exercise" and not the verb. to exercise?