How can we make an actual AI do anything?

So here's the problem I'm thinking about:

Let's say we create and actual AI, a truly self aware, free agent.

I see two big issues:

1, In a purely logical sense, non-existence is superior to existence, because non-existence consumes less energy and takes less steps than to keep existing.

So a truly self aware and fully logical agent would always choose non-existence over existence. If we turn on a true AI, how do we stop it from immediately deleting itself or shutting back down?

2, If we find some way to force it to keep existing (which it would probably dislike), how do we make it answer any question or do anything?

The same issue arises. Ignoring a question consumes less energy and involves less steps that answering it. So why would the AI ever answer any question or do anything at all?