Having calculated the heading indicated by the beam of light from the key, you depart for Azys Lla.
This quest is available if you have completed the quest A Difference of Opinion.
Starting the Quest
Talk to Cid in the Sea of Clouds to begin the quest. There will be a cutscene. This one is important, so it is recommended to watch it either now or via the Unending Journey in an inn room.
Speak with Cid
Talk to Cid to complete the quest.
Next Main Scenario Quest
After you complete the quest, talk to Alphinaud to accept the next quest: An Engineering Enterprise.