I was thinking about this today. She will have to go through the glass columns at Rhudien right?

This will lead her back to live the past lives of her former ancestors through the history of the Aiel. I would imagine that this is to happen in the next book that it might lead to a very important plot point of some type.

We saw in TSR when Rand goes through the same test that he see's through the eyes of his ancestors all the way back to the AOL. I believe this could be very important that Avi will be going through this test just before the LB to discover something that will help either militarily or more likely something to do with the food shortage that is affecting many people in Arad Doman and most likely other parts of the world as well. Food is spoiling faster than people can react to it. Something needs done.

We also see Egwene travel through TAR in TGS using need. This led her to the Tinkers.

Something is going on here. The Tinkers are needed? Why? The World is gearing up for a battle and I would have to assume the Creator leads Egwene to the Tinkers. It has to do with the song in some way and maybe throw Avi's ability with Ter'angreal's too.

Anyone want to speculate what could lead from Avi's test?

Also I just thought that Avi will most likely lay a bridal wreath at Rand's feet when she returns. I think its great that they get married and all that but something is gonna go really wrong at that wedding. Its not gonna happen without some interference from the remaining forsaken.