No military action at all is precisely the strategy that has been practiced by both sides since the cease-fire in 1953. There is no reason to think that this strategy would suddenly change now.

Neither side has anything to gain by conflict. The North Korean government may be evil but they are not stupid-- they realize that if they attack their regime will be destroyed. Similar, the US military knows that if they attack first, they will antagonize China, destabilize the region, and cause thousands of unnecessary deaths for South Korea.