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While I would usually agree that using force is a bad option, NK is a unique situation where if the government fell they could start reuniting them with the South. Think of it more like east berlin and west berlin reuniting.

The American government couldn't give a crap about the NK people, they are just using this as an excuse to build bases and fill them with missiles on China's boarder. With a added bonus of a different angle to threaten Russia with their stinking missiles.