Does Wu not mean non-being or emptiness?
Then acting from emptiness = Wu Wei is the most accurate translation.
Means acting without self-interest.
Doing means when self is active and doing things with intention to reach a goal.
Nature as spoken of here is your True Nature, The Golden Elixir as named in some Taoist texts.
All we are doing here is going back to that nature by whatever practice we deem necessary. Some people overlook it because it is invisible, non-tangible and might appear mundane.
It is the opposite of passion, excitement and entertainment for the mind.
The seeking for it is the impulse coming from itself. Listen to this voice. See where it is coming from.