What are the elements of a First Amendment retaliation claim?

"[P]risoners have a First Amendment right to file prison grievances" and to be free from retaliation for exercising this right. Brodheim v. Cry, 584 F.3d 1262, 1269 (9th Cir. 2009); Rhodes v. Robinson, 408 F.3d 559, 567 (9th Cir. 2005). There are five elements to a First Amendment retaliation claim: "(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 reasonably advance a legitimate correctional goal." Rhodes, 408 F.3d at 567-68.