Both of the adverbs 一齐 and 一同 have the same meaning “together”.
The adverb 一齐 indicates that everyone completed an action at the same time or in unison.
The adverb 一同 indicates that everyone completed an action at the same time and in the same place. It can also be translated as “alongside”.
We should state them both before the predicate, which is expressed by a verb or a verb phrase.