When you arrive at Remiem Temple, save. I will note that it’s a little pointless to bother with what’s within the temple for now. While you can technically work on a new Summon here (and the best one at that), we’re far off from being able to complete the quest. (By the way, it’s a super-Belgemine gauntlet.) Another section, another time. Look for the detailed guide in the Side Quests section.
The main reason we’re here, then? Left of the Save Sphere should be Al Bhed Primer Vol. XXIV . Also nearby should be a Chocobo! (Dunno why I love those cute li’l birds so much.) If you ride it, you get to do a race. While completely optional, the rewards are grand enough to warrant covering it now.
In any case, you will be in a race against another Chocobo in a set of winding, ever-smaller circles to the end. If you win, by definition you get the Cloudy Mirror . Nice as that is, we still can’t properly use it for now until we get the Airship and can work on the Celestial Weapons. However, you can open chests on the way to get other rewards: one chest yields an Elixir , two yields a Megalixir , and three yields 30 Wings to Discovery ! You can have Rikku Mix two of these to create the Trio of 9999 item, which makes every action your party does do 9,999 damage/healing (or more, if it normally would do more).
A brief sidequest, but it’s well worth it if you get all three chests.