He who acts without any thought of being the actor is unstained by action, even in the midst of the busiest life
The teaching separates the ordinary sense of "I am doing this" from action itself, arguing the doing can continue while the doer-feeling simply isn't there.
Ashtavakra's target throughout chapter eighteen is the assumption baked into ordinary language — that behind every verb there must be an "I" performing it. He argues the enlightened person keeps working, eating, speaking, and responding to whatever life presents, but without the accompanying sense of personal agency that usually rides along with action. Because the stain of karma, in this view, comes from identifying with doership rather than from the act itself, a person who has dropped that identification remains untouched no matter how active or demanding their life looks from outside. It's a claim about interior experience, not about becoming passive — the busiest life and the stillest mind are held to be entirely compatible.
Ashtavakra Gita