The vision that Egwene had in the third part of her accepted test will true. Remember that she had the ter'angreal ring with her and the arches were going haywire.
So here's what will happen. The result of Egwene's army attacking Tar Valon will set up 2 rival halls in the tower with Egwene as the Amyrlin. It was mentioned casually in PoD that there was once 2 rival halls in the Tower. Elaida, with Alviarin's assistance, will head the rival hall. Rand will somehow get his hand in there and Egwene will get pretty mad that he will be trying to run the Tower. he will face her and know her anger.
As a result of this he will leave but something will happen to sheriam and beldeine, the Aies Sedai sworn to rand will become Keeper. Remember that Beldeine was Keeper in Egwene's accepted test.

Then the Black Ajah will rise up and turn Elaida Black, depose egwene and beldeine, and then capture Rand. And this is where we start out with egwene in her test. remember she also says that she never held the oath rod, and so far she hasn't.

this will also be the part where gawyn has to kneel to egwene or break her back. he will probably stay in the tower through all this and get together with egwene but remain loyal to Elaida. Egwene will need him to help her save Rand.

So that's my theory. I don't know what will happen with seaine and pevara's black ajah hunting mission though.