What strategy did the united states use when it entered the korean war?

dropping atomic bombs to force the north koreans to the peace table
convincing the south koreans that they should sign an armistice
sending forces behind north korean lines and landing at inchon
offering massive foreign aid if north korea promised to stop fighting

The answer would be: sending forces behind North Korean lines and landing at Inchon. 
On June 25, 1950, North Korean forces marched across the 38th parallel - the line of latitude that separated the North and South. President Harry Truman interfered with the support of the United Nations and tasked General McArthur to lead the UN troops. He then succeeded an amphibious attack on September 15, 1950, and landed at Inchon. On September 27, 1950, UN troops recapture Seoul, the capital of South Korea. On October 9, 1950, South Korean and UN troops drive North Korean forces back across the 38th parallel.