What is the test for determining whether a court committed plain error by failing to correct an error?

To conclude that a court committed plain error, we must find an "(1) error (2) that is plain and (3) affects substantial rights." United States v. Villafuerte, 502 F.3d 204, 209 (2d Cir. 2007).² If these three conditions are met, "we then must consider whether to exercise our discretion to correct [the error], which is appropriate only if the error seriously affected the 'fairness, integrity, or public reputation of the judicial proceedings.'" Id. (quoting United States v. Doe, 297 F.3d 76, 82 (2d Cir. 2002)).