Question

What action of Russia prompted Germany to declare war?

Answer 1

The support of Russia to Serbia against the Austo-Hngarian Empire.

Explanation:

After the assassination of Archduke Franz Ferdinand, Austria sent an ultimatum to Serbia that was basically unacceptable and led to a declaration of war.
Serbia call for help was answered by her traditional ally, Russia, that started to mobilize troops to fight Austria. Germany intervened sending another ultimatum to Russia (the Kaiser and the Tsar were cousins!) to suspend her intervention to support Serbia AND to France prompting not to help Russia.
When these ultimatums were ignored Germany declared war (1914).

It is incredible to see the "Domino Effect" of alliances that triggered intervention in a war that was basically started by an assassination in a faraway country and involved all the European nations!