What is the test for a First Amendment claim against a public employer?

To state a First Amendment claim against a public employer, "'an employee must show: (1) the employee engaged in constitutionally protected speech; (2) the employer took 'adverse employment action' against the employee; and (3) the employee's speech was a 'substantial or motivating factor for the adverse action.'" Lakeside-Scott v. Multnomah County, 556 F.3d 797, 803 (9th Cir. 2009) (quoting Marable v. Nitchman, 511 F.3d 924, 929 (9th Cir. 2007)). Castle did not take an adverse employment action against plaintiff, as discussed below (see page 17 infra), and therefore her claim fails as a matter of law. Even if he did, Castle is immune from liability.