Since some of the things that Four would be looking into are already being covered by other people, he's going to be looking into the nature of the World Tree. He's fairly certain it's not an ordinary tree - or even necessarily a physical tree - and given that he's got some familiarity with things that are central to something's well-being (particularly the Eye of Harmony), he'll be looking into any and all records of what either stabilizes or destabilizes the World Tree.

As something of a back up option in case things go badly wrong, he's also going to be looking into if would be possible or feasible to maintain the world(s) on sheer force of will, in the vein of Omega and the Anti-matter universe. He doesn't expect to have a lot of luck there, though.