how should he use this knowledge he gained to his advantage to save annabeth

Bide his time because nothing he knew was immediately beneficial

As much as being privileged to be one of the few mortals to see or know that there are more than one Pantheon alive Percy couldn't do that much.

Even as a demigod, from what Artemis pointed out directly, other pantheons hate each other. And it makes sense in a way.

If belief is power, and holds the power to capture enough of the publics imagination to retain their power even if their belief has wayward, then they would fight for every scrap they have.

What was he going to do?

walk right down to Rome itself and radicalize people to fight for a cause that he didn't even know if they knew about?

let alone were they willing to offer their wayward amount of people. From what she even described there was a colony there. Far greater than what they had.

A retirement home for demigods. Oh that was a dream for him. .

However this was a more pressing issue. He couldn't quite keep Artemis if the Olympians found out what happened they would surely kill him. He was fucked if he didn't deal with that