Precious Yearnings

Precious Yearnings is a Blade Quest in Xenoblade Chronicles 2. It can be received from Agate in the in Fonsa Myma, Kingdom of Uraya, after unlocking Agate's second Key Affinity reward and resting at Folmarie Inn, provided Nia, Tora, Mòrag, Zeke, Pyra and Agate are in the party. Completing some of the quest's objectives will unlock Agate's third and fourth Key Affinity reward while completing it will unlock her fifth Key Affinity reward.

Quest objectives

 * Look for a new type of ore at the Old Quarry, Uraya.
 * Meet Misimisi the jeweler at Argentum Trade Guild.
 * Search each region for new types of mineral and have Misimisi appraise them for you.
 * Search for a new mineral in a Titan in a land which is yet unexplored by others.
 * Investigate the cliffs in the Womb Hollow in the Land of Morytha.
 * The prospection site requires clearing a Prospecting level 3 check and is guarded by one Elidor Parisax, two Leran Parisax and three Mabalus Parisax.
 * Have Misimisi appraise your mineral at Goldmouth Flight Deck, Argentum.

Results
"After appraising the ore, a new mineral is discovered. Agate names it after herself."