Answer:
He offers to swear a binding oath.
He tells the swineherd something that only he and Odysseus knew.
Step-by-step explanation:
These are the two actions that Odysseus takes in order to convince the swineherd that Odysseus is coming back. Upon returning, Odysseus visits the people he cares about while wearing a disguise. This helps him examine the current situation without being discovered. As he visits the swineherd, he refuses to believe that Odysseus will be back, as he believes him to be dead. Odysseus then swears a binding oath and tells the swineherd something only he and Odysseus knew in order to convince him of his return.