What approach, if any, should the United States take in regards to the situation in Syria?(intervene alone, intervene with NATO, not intervene at all, provide covert assistance to rebels, etc.)?
I would argue that the United States should not intervene at all. If it does intervene, it should only be to provide covert assistance to the rebels.
It is not at all clear that it is in our interests for the rebels to win. At the same time, it is not in our interests for the Assad regime to continue to misrule Syria as it does. It may be that the best thing for the United States (looking at this in a cold-blooded way) is for the conflict to last a long time and for it to damage Syria badly.
Morally, of course, this is not an attractive policy. However, it is often the case that foreign policy is made based on considerations of power rather than morality. It is also the case that a win by the rebels might not necessarily bring about a government that is any better than the current regime.
Since there is no clear-cut "good guy" in this battle, we would be better off staying out of it.