Question: Did the Battle of Pusan Perimeter or the Battle of Peleliu happen first?

full_context: Document 1: Battle of Taegu: The Battle of Taegu was an engagement between UN and North Korean forces early in the Korean War, with fighting continuing from August 5–20, 1950 around the city of Taegu, South Korea. It was a part of the Battle of Pusan Perimeter, and was one of several large engagements fought simultaneously. The battle ended in a victory for the United Nations after their forces were able to drive off an offensive by North Korean divisions attempting to cross the Naktong River and assault the city.
Document 2: Peleliu: Peleliu (or Beliliou) is an island in the island nation of Palau. Peleliu forms, along with two small islands to its northeast, one of the sixteen states of Palau. The island is noted as the location of the Battle of Peleliu in World War II.
Document 3: Battle of P'ohang-dong: The Battle of P'ohang-dong was an engagement between the United Nations and North Korean forces early in the Korean War, with fighting continuing from 5–20 August 1950 around the town of P'ohang-dong, South Korea. It was a part of the Battle of Pusan Perimeter, and was one of several large engagements fought simultaneously. The battle ended in a victory for the United Nations after their forces were able to drive off an attempted offensive by three North Korean divisions in the mountainous eastern coast of the country.
Document 4: Battle of the Bowling Alley: In the Battle of the Bowling Alley (August 12–25, 1950), United Nations (UN) forces defeated North Korean forces early in the Korean War near the city of Taegu, South Korea. The battle took place in a narrow valley, dubbed the "Bowling Alley", which was north of Taegu. It followed a week of fighting between the Korean People's Army (KPA) 13th Division and the Republic of Korea Army's (ROK) 1st Division along the latter's last defensible line in the hills north of the city. Reinforcements, including the US Army's 27th and 23rd Infantry Regiments were committed to bolster the South Koreans' defenses. This battle and several others were smaller engagements of the Battle of Pusan Perimeter.
Document 5: Battle of Peleliu: The Battle of Peleliu, codenamed Operation Stalemate II by the United States military, was fought between the U.S. and the Empire of Japan during the Mariana & Palau Campaign of World War II, from September to November 1944, on the island of Peleliu.
Document 6: Battle of Pusan Perimeter: The Battle of Pusan Perimeter was a large-scale battle between United Nations and North Korean forces lasting from August 4 to September 18, 1950. It was one of the first major engagements of the Korean War. An army of 140,000 UN troops, having been pushed to the brink of defeat, were rallied to make a final stand against the invading North Korean army, 98,000 men strong.
Document 7: Battle of Okinawa: The Battle of Okinawa (Japanese: 沖縄戦 , Hepburn: Okinawa-sen ) (Okinawan: 沖縄戦 , "Uchinaa ikusa " ), codenamed Operation Iceberg, was a major battle of the Pacific War fought on the island of Okinawa by United States Marine and Army forces against the Imperial Japanese Army and included the largest amphibious assault in the Pacific War during World War II, the April 1, 1945, invasion of Okinawa itself. The 82-day battle lasted from April 1 until June 22, 1945. After a long campaign of island hopping, the Allies were planning to use Okinawa, a large island only 340 mi away from mainland Japan, as a base for air operations for the planned invasion of the Japanese home islands.
Document 8: Battle of Battle Mountain: The Battle of Battle Mountain was an engagement between United Nations (UN) and North Korean (NK) forces early in the Korean War from August 15 to September 19, 1950, on and around the Sobuk-san mountain area in South Korea. It was one of several large engagements fought simultaneously during the Battle of Pusan Perimeter. The battle ended in a victory for the UN after large numbers of United States (US) and Republic of Korea (ROK) troops were able to prevent a North Korean division from capturing the mountain area.
Document 9: Battle of Guam (1944): The Second Battle of Guam (21 July – 10 August 1944) was the American recapture of the Japanese-held island of Guam, a U.S. territory in the Mariana Islands captured by the Japanese from the U.S. in the 1941 First Battle of Guam during the Pacific campaign of World War II.
Document 10: Battle of Ka-san: The Battle of Ka-san was an engagement between United Nations (UN) and North Korean forces early in the Korean War from September 1 to September 15, 1950, in the vicinity of Ka-san in South Korea. It was a part of the Battle of Pusan Perimeter, and was one of several large engagements fought simultaneously. The battle ended in a victory for the United Nations after large numbers of United States (US) and Republic of Korea (ROK) troops repelled a strong North Korean attack.
Document 11: Kunio Nakagawa: Colonel Kunio Nakagawa (中川 州男 , Nakagawa Kunio , 23 January 1898 – 24 November 1944) was the commander of Japanese forces which defended the island of Peleliu in the Battle of Peleliu which took place from 15 September to 27 November 1944. He inflicted heavy losses on attacking U.S. Marines and held Peleliu Island for almost three months. On the evening of 24 November, after the battle was lost, he committed "seppuku" (ritual suicide) in the tradition of Japanese samurai warriors. He was posthumously promoted to lieutenant general.
Document 12: Battle of Angaur: The Battle of Angaur was a battle of the Pacific campaign in World War II, fought on the island of Angaur in the Palau Islands from 17 September—22 October 1944. This battle was part of a larger offensive campaign known as Operation Forager which ran from June 1944 to November 1944 in the Pacific Theater of Operations, and Operation Stalemate II in particular.
Document 13: Battle of Iwo Jima: The Battle of Iwo Jima (19 February – 26 March 1945) was a major battle in which the United States Marine Corps landed on and eventually captured the island of Iwo Jima from the Imperial Japanese Army during World War II. The American invasion, designated Operation Detachment, had the goal of capturing the entire island, including the three Japanese-controlled airfields (including the South Field and the Central Field), to provide a staging area for attacks on the Japanese main islands. This five-week battle comprised some of the fiercest and bloodiest fighting of the Pacific War of World War II.
Document 14: Battle of Pusan Perimeter logistics: Logistics in the Battle of Pusan Perimeter (August 4 – September 15, 1950) during the Korean War played a decisive role in the battle. Efficient logistics, the management of personnel and materiel, supported United Nations (UN) supply lines while the North Koreans' routes of supply were steadily reduced and cut off. UN logistics improved throughout the Battle of Inchon and the defeat of the North Korean army at Pusan.
Document 15: Battle of Masan: The Battle of Masan was an engagement between United Nations (UN) and North Korean (NK) forces, which took place early in the Korean War between August 5 and September 19, 1950, in the vicinity of Masan and the Naktong River in South Korea. It was part of the Battle of Pusan Perimeter, and was one of several large engagements fought simultaneously. The battle ended in a victory for the UN after large numbers of United States (US) and Republic of Korea (ROK) troops were able to repel the repeated attacks of two North Korean divisions.
ground_truth: Battle of Peleliu