Rand chases down Couladin, faces his down, and gets that bit resolved, then brings the Aiel to war against the lands west of the Three-fold land. At the end of the book, he's married Elayne, and is on the throne of Camelyn. He also defeats Sammael, having learned from Asmodean. More sexual tension with Lanfear, but no coital activies (sorry, Roy).
Perrin goes awandering again, with Faile & Aram, and ends up finding the song.
Siuan Sanche and Leane catch up with Elayne/Nyneave/Seanchan and track the BA a little more. The escaped false dragon ends up with the BA (Taim? Is that who it was?). The BA continue to elude them.
Elayne learns more about the dreamworld, and she and Perrin track down "Slayer" somewhat, but don't catch him. (Isam is going to have to have a showdown with Lan).
Mat gets capture in the hopes of getting Rand to follow along, and is taken to the courts of the nine moons.
Who am I forgetting? Lan meets up with Isam, Moiraine clashes with Eleida, and uh ... that's pretty much it.
Now, 'bout the "fires of heaven". My best guess is that Rand (with the one massive sa'angreal) and Lanfear (with the other) have a little tiff. *grin*
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