Is there a verb that can replace "waste" in the original phrase to get the opposite meaning? For instance, wouldn't it sound awkward if I say "I used all the chances I've been given"?
"Avail" is your word, or is pretty close. It means "to use or take advantage of (an opportunity or available resource)" (Google). But to use it you'd need to change your sentence slightly, because it acts on individuals that are phrased as objects. For example, I availed myself of all opportunities.