Suppose a group of intelligent but insane people has developed mind control technology. They have managed to plant a chip inside the US president's head. They can wirelessly send signals to his mind and he will obey them without question. The president is as rational as before, and perform his day-to-day tasks as before. When he receives an instruction, his own counter-reasoning shuts off and he obeys the commands. He is still rational in understanding the commands, also behaves rationally, making it almost impossible for a common man to notice. However a series of tests by a psychologist will probably reveal the mind control. So will an operation on his brain.
If the group wants to eliminate as much of the human race as they can (even including themselves), what would be the best strategy* to do so? Would it be to just ask the president to try bombing the whole world with nukes**? Or will it be a more planned and subtle approach that makes use of the other powers of the president?
*Best may be hard to determine, so any good strategies are welcome.
**Using nuclear weapons requires approval of a second person, so it will take some planning even to get access to the nukes.