In the Iliad, what role does Nestor play in the argument between Achilles and Agamemnon?

After the chieftains have had their fill of food and drink, Nestor advises Agamemnon to make peace with Achilles so that he will rejoin the fighting. Agamemnon agrees that it was madness that made him insult their greatest warrior, and prepares an offer for Achilles. He will give the great warrior fabulous riches, including one of Agamemnon's own daughters as wife and seven of Agamemnon's citadels, if only he will return and "yield place to me, inasmuch as I am the kinglier" (9. 160). Nestor proposes sending Phoenix, Great Ajax, and Odysseus, as well as the heralds Odius and Eurybates.