SEOUL, South Korea — North and South Korea agreed Friday to hold military and Red Cross talks later this month on reducing tensions and resuming reunions of families separated by the 1950-53 Korean War. The rivals also agreed at a meeting of senior officials at the border village of Panmunjom to establish a liaison office at the North Korean border town of Kaesong and hold sports talks on fielding combined teams for some sports at the Asian Games in August, as they continue to take steps toward reconciliation. South Korea says building trust with North Korea is crucial amid a U.S.-led diplomatic push to persuade the North to give up its nuclear weapons. The high-level meeting between the Koreas followed talks in New York between U.S.