Assumedly is a relatively uncommon word that means "presumably" or "supposedly". Some synonyms for assumedly include the words "allegedly", "apparently", "ostensibly", and "presumptively". These words all convey a sense of likelihood or possibility, rather than certainty. Other potential synonyms for assumedly include "putatively", "reportedly" and "purportedly". All of these words may be used to indicate that something is believed to be true, but that there is some uncertainty or ambiguity attached to the statement. As with any synonym, it's important to consider the context in which the word is being used, and to choose the most appropriate word based on the meaning and tone of the sentence.