We quickly dispatched the Efreeti and fire elementals. During its demise, the Efreeti informed us that its leader (?) Archimedes is already inside the challenges and has a large head start on us. Turns out the fire elementals were coming from a magic item that Crestin found. After the combat, we rested for a short time and made our way beyond the original symbols. Once inside we the following:
Reform
Reuse
Reincarnate
Sounds like actions done with a Volcano, so I have to imagine these trials have a lot to do with fire.
After passing the new symbols we came to a room with a lot of holes, creatures began coming out of the holes to attack us. Turns out we needed to send these creatures back down the holes to cause the ground and ceiling to rise. This allowed us to find an opening that led to the next section of this upper room. What we will find next we don't know, but we will need to make a bit of haste if we want to catch up with the Efreeti's boss.