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This is probably an abuse of terminology, but I think "action" feels more perfective and "activity" feels more open/continuous.

So, to run to the shop is an action. You start running, you get to the shop, you stop. It's closed, complete, there's a final result. Opening a door is an action, writing your name is an action, eating a piece of toast is an action.

An activity is where the focus is on the present-tense, instantaneous state of *doing something*. Running, as exercise, is an activity. You don't particularly care about where you're going, the point is simply to be moving fast. Writing, as something to occupy your time, is an activity. Eating at a buffet might be an activity - you're not necessarily there to eat a meal, which would be an action, you're just there to *be eating*.

In these examples, forgetting is an action and living in a city is an activity. Although nobody would ever describe living in a city as an activity outside of this kind of grammar talk :) but it has the sort of continuous, open, being-in-a-state feel that activities have.

Complete/completed: here, they're interchangeable. "Complete" means that something is full, whole, intact, includes every part. "Completed" means that it *has been made complete*.

I think anywhere you'd use "completed" as an adjective, you could use "complete" - if I were building a model car, I could say "and here is the completed model" (because it was incomplete, then I worked on it until it was complete) or I could say "and here is the complete model".

But it doesn't always work the other way around - you can say "she offered me complete control of the project" because she offered you full control, there is no element of control that she didn't offer. But you can't say "she offered me completed control", because the sense of *assembling* something isn't there.