Once in the next room, there is a short scene where you rescue Vivi. Make sure you update his equipment and abilities then head to the door to the north.
To the right of the door is a chest with 95 Gil (H). Examine the door (6) and choose to open it. You will have a mandatroy battle against 3 Ghosts. Afterwards, you will enter the room.
There is a machine to your right that you can examine but there are 3 chests in here: The first is right in front of you which contains a Phoenix Down (I), to the right of that, slightly behind the machine is a Potion (J).
Finally, completely to the right, hidden behind the machine is a Phoenix Pinion (K).
Exit the room. You can examine the machine in here too but head right across the bridge (7).
In the next room you can examine the machine in 3 locations; The conveyor belt, the machine before the tunnel in the north and inside the tunnel.
Continue north and exit into the next room where a scene will play.
Following this, the scene will move to Steiner who is at the Observatory. After the short scene, head down the stairs, wait for the man to enter the house and follow him inside. Talk to him then leave the house.
Leave the area. You will be out on the plain where you will see the Cargo Ship.
After a short scene, choose "poke it with a sword".
After another short conversation, you will face another Black Waltz Boss.