Well, for anyone curious about history, the answer is "very little" because it does no longer depend on the president, but on the whole country. Or so I see it.

And it becomes fairyland quickly because so many things that would have to happen are not going to happen without the whole country stepping up and behind a new power.

That's why the American president in this manner is quite worthless. But to answer your question, the thing s/he could do would be just that, unify the country behind a morally good idea. Anything else just won't change what we think about the usa for the better.

So, unify the country behind a new democratic system. Then give it a decade or two!