You do not need to cause the mess to become capable of cleaning your part.

You can clean up something you did not cause without that meaning you accept blame for it. People sometimes refuse to act because acting feels like admitting fault, and the mess stays. Separating the two frees you to be useful without giving anything away.

If there is a situation you have been leaving alone on principle, ask whether your part could be addressed without conceding anything. Say plainly, if needed, that you are handling it and that it was not your doing. Both things can be true out loud.