Final answer:
The runner on second with 0 outs must stay on the base and tag up after a fly ball is caught. They can then attempt to advance to third base if it is safe.
Step-by-step explanation:
If you're the runner on second base with 0 outs on a fly ball to left/center field, the correct action is a) Stay on second base and tag up after the catch. Once the outfielder catches the ball, you can advance to third base if it is safe to do so. This is because you must tag up, which means you must touch the base after the catch is made before you can legally run to the next base. Attempting to advance without tagging up can result in being called out. The situation dictates the best course of action after tagging up; for example, you might stay at second if the catch is made close to third base or if the outfielder has a strong arm.