What are the elements of a claim of retaliation in violation of the First Amendment?

A viable claim of retaliation in violation of the First Amendment consists of five elements: "(1) An assertion that a state actor took some adverse action against an inmate (2) because of (3) that prisoner's protected conduct, and that such action (4) chilled the inmate's exercise of his First Amendment rights, and (5) the action did not reasonable advance a legitimate correctional goal." Rhodes v. Robinson, 408 F.3d 559, 567 (9th Cir. 2005); accord Brodheim v. Cry, 584 F.3d 1262, 1269 (9th Cir. 2009). A plaintiff suing for retaliation under section 1983 must allege that "he was retaliated against for exercising his constitutional rights and that the retaliatory action does not advance legitimate penological goals, such as preserving institutional order and discipline." Barnett v. Centoni, 31 F.3d 813, 816 (9th Cir. 1994).