assume / presume
Taking something as true versus taking it as true on firmer ground.
Assume is the general word for taking something as given, often without proof. Presume is stronger: you take it as true because you have reason. In law, presumed innocent is the set phrase. In ordinary use the two overlap; assume is the default.
Examples
UseLet’s assume the train is late.
UseI presume she got home; her coat is here.
AvoidLet’s presume the train is late. (If you have no reason yet.)