"This burden is one of production, not persuasion; it 'can involve no credibility assessment.'" Reeves, 530 U.S. at 142 (quoting St. Mary's Honor Ctr. v. Hicks, 509 U.S. 502, 509 (1993)); accord Vaughn v. Woodforest Bank, 665 F.3d 632, 636 (5th Cir. 2011); Alvarado, 492 F.3d at 611. "The [employer] must clearly set forth, through the introduction of admissible evidence, reasons for its actions which, 'if believed by the trier of fact,' would support a finding that unlawful discrimination was not the cause of the employment action."