If you need to reacquire these items (if you drop them or fail to defeat the NM), you can purchase them from these NPCs. Aeka will demand one Darksteel Ore for payment, and Ranemaud will want one Platinum Ore and two Gold Ore.
Using the Sacred Sprig and Oriental Steel, you must now retrieve the Sacred Branch and Bomb Steel. The following two steps can be done in either order.
If multiple players in a party are completing this quest simultaneously, only one of them needs a hatchet.
At K-10 there is a pathway which leads to an unmapped area. Continue east straight to L-10 where you will see a large tree. There are rocks at the base of the tree that you can climb up in order to get close enough to the ??? to initiate the next sequence.
Trade or use your hatchet on the ??? and a Guardian Treant will spawn. (Your hatchet will not be consumed.)
The Mumeito is used during the Samurai AF Great Katana quest (The Sacred Katana). It is advisable to hold on to this weapon in storage; if it was dropped you will need to pay Ranemaud 30,000 gil in order to obtain a new Mumeito after you have accepted the quest.