human
This is likely vastly oversimplifying things but...
I think a smart leader would respond to a nuclear strike from NK not with a retaliatory strike in kind but with a deliberate response with conventional forces.  It demonstrates to the world that the US is not only capable of taking out a mad dictator but also wise with its nuclear arsenal.  This would be especially true if the missile defense works as it should and destroys any incoming attacks.
There's also the added bonus that China and Russia couldn't say anything beyond trying to claim the US "provoked" a nuclear strike and we wouldn't be bogged down in a territory that is completely ignorant of democratic principles as the reunification of Korea would like occur as a result and be under SK's governance.  The only concern (other than the typical insurgency that'll result from the fallen regime) is corruption which SK still suffers from.
Unfortunately we don't have a smart leader in the WH.
gpt
{"moderation": ["toxicity", "insult"]}