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This led to a series of presidential decisions—most famously order number 12,333, signed by Ronald Reagan in 1981—which barred assassinations.
The real force of such orders was to squelch rogue plots hatched in the lower levels of the security services; procedures still exist for the president, in consultation with congressional leaders, to authorise the killing of a perceived adversary.
So the US can still carry it out, so long as they have a cup of tea and a chat first. Way to go! :)