How the fuck do I lane against Kassadin?

I know I shouldn't have that much trouble, but I do. It feels like I can only ever AA harass him because shield and passive soak up any damage I can do with abilities. Even If try to zone him with aas, he just Q's me and out trades me. Just whittles me down and then all in's me at level six and I can't do ANYTHING from that point on because half of the damage he doesn't dodge with his ult is mitigated by passive and Q. Afterwards he just outroams me and snowballs his other lanes. Advice plez :////
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