Logically, the best course for the United States is not to engage. IS is beginning to realize this and seemingly prefers to force a battle. That is why we are beginning to see terrorist actions flaring in Western countries. The lesson al-Qaida taught IS is that the Americans have a threshold and that if you cross it, they will react dramatically.
Therefore, it appears to me that IS is searching for that threshold and probing to see responses. Attacks like the ones in Paris last month were not in response to French involvement in the region. These attacks are unconnected to that, but are designed to be as terrifying as possible—both in their suddenness and brutality—and compel a response.