What two German actions caused US to enter world war 1?

It was actually one action, and one diplomatic overture.

Germany was attacking neutral US ships without warning, after promising not to. And in an apparent attempt to deflect the US, the Germans offered an alliance to Mexico, as detailed in the Zimmerman Telegram intercepted by the British.

The Germans sunk the Lusitania believing that it carried supplies to Britain as well as arms in order to help the war effort. It was carrying some American passengers when it was torpedoed, and this led to America joining the war. However, Germany may have been justified, as the ship may have actually been supplying Britain with much needed supplies in direct disregard of the sanctions imposed by Germany. In any effect, both the Lusitania and the Zimmerman affair swung American popular opinion in favor of interceding (effectively) in the conflict.