assume has 21 distinct synonyms spread across 8 of its 9 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
take to be the case or to be true; accept without verification or proof
“I assume his train was late”
take on titles, offices, duties, responsibilities
“When will the new President assume office?”
take on as one's own the expenses or debts of another person
“I'll accept the charges”
take up someone's soul into heaven
“This is the day when Mary was assumed into heaven”
Synonyms, antonyms and the broader and narrower relations for assume come from Princeton University’s WordNet. Full sources and licences.