Final answer:
The Athenians turned to the 'Mysteries of Samothrace', a ritual passed down from the Pelasgians and celebrated by the Samothracians.
Step-by-step explanation:
The English term for the ritual that the Athenians turned to after receiving Pythia's first answer about Xerxes' invasion is the 'Mysteries of Samothrace'.
These rituals were celebrated by the Samothracians and had been passed down from the Pelasgians who previously lived in Samothrace and cohabited with the Athenians. The Athenians were the first Greeks to make ithyphallic Herms, and they learned the practice from the Pelasgians.
The Mysteries of Samothrace, along with other Greek rituals, were a source of inspiration for the Athenians when seeking help from a more powerful entity to defend against Xerxes.