What event was held on 27 May 2013 that featured one team that also competed in the League Cup and FA Cup?
2013–14 Crystal Palace F.C. season The 2013–14 season is Crystal Palace's first season back in the Premier League after 8 years. They clinched their place in the top tier with a 1–0 victory over Watford in the 2012–13 Championship Play Off Final. Palace spent eight seasons in the Championship after being relegated from the Premier League in the 2004–05 season. Crystal Palace also competed in the League Cup and the FA Cup.
1989–90 Birmingham City F.C. season The 1989–90 Football League season was Birmingham City Football Club's 87th in the Football League and the first in their history in which they played in the third tier of the English football league system. After a sound start to the season, with six wins from the first ten games, their results worsened, and they eventually finished in seventh position in the 24-team Third Division, three points outside the playoff places. They entered the 1989–90 FA Cup in the first round proper and lost in the third, eliminated by Oldham Athletic after a replay, and entered the League Cup at the first round and lost in the second, beaten 3-2 by West Ham United over two legs. They lost in the preliminary round of the Football League Trophy, a competition open to teams in the third and fourth tiers of the League.