rage blade, the new upgraded hexgun thing that has a 300 magic damage attack with a slow, rylais, zhonyas.
burst comes from magic, as said. passive increases the damage from your normal attacks enough, end game akali normal attacks are doing like 220+150 magic damage.
however, I have reached the point before where i was very very fed, and had like 85% extra magic damage added to physical and said screw it and bought a bf sword lol. But you'll find that with the targets you should be picking out, you will likely do very little auto attacking aside from when you decimate a tower with extreme pwnage.