Rand has been talking for some time about cleansing the taint. LTT seems to be terified by the prospect of attempting this. Rand knows that the only sa'angreal left, (after he discovers the flaw in Callandor) which could do this is the statue. However, I believe that he could only do this if an incredibly strong female channeler uses the other statue. Enter Nyneave. Rand will tell N about the statue, get the figurines from rhuidean, and he and N will link and cleanse Saidin.