Killing blindly and randomly doesn't seem like the best strategy. I think I have a better idea that takes advantage of our numbers. We don't necessarily need to kill the cultists-- just the possessed. Therefore, all we need to do is find the possessed (and a 2nd and 3rd time if necessary). We split into 3 public groups, let's call them Groups A, B, and C.
Group A passes. The other groups unveil all the members of Group A at a 2:1 ratio-- one member from Group B and one member from Group C all pick the same person from Group A. The possessed cannot pass their turn-- it changes to an attack. If nobody is attacked, then the members of Group A are all not the possessed. If they do any other action than passing, then we know they are the possessed, or a cultist trying to hide the possessed, and we can just kill them.
Repeat the next day with Group B, and then the next with Group C.