The Second Continental Congress took several significant actions, including issuing the Declaration of Independence in 1776. They did not pass the Intolerable Acts; those were enacted by the British Parliament in response to the Boston Tea Party. Additionally, while they did send a petition to King George III, specifically the Olive Branch Petition in 1775, it was not their most defining action. "Common Sense" was written by Thomas Paine but was not authored by the Congress itself.
So, the most notable action of the Second Continental Congress among the options you provided is that they issued the Declaration of Independence.