What ceremony was instituted at the Last Supper?

Synoptics: The Eucharist (Matt. xxvi, 26–28; Mark xiv, 22–24; Luke xxii, 19, 20).

John: The washing of feet (xiii, 4–9).

John does not mention the former ceremony, and the Synoptics do not mention the latter; yet each is said to have been performed immediately after supper.