The biggest problem that John Adams faced during his presidency was the state of undeclared war that existed between the United States and France. Ever since the conclusion of the Jay Treaty between America and Great Britain in 1795, France had been hostile towards its former ally. France's increasing aggressiveness towards the United States created a headache for Adams, who had to figure out a way to respond without becoming embroiled in a full-blown war.
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President Theodore Roosevelt sent troops to support Panamanian rebels in the fight against Colombia so that the Colombians would grant the United States the rights to build a canal, which was in the best interest of the US.