nope, avenge is only a verb. In this sentence the verb phrase is “shall be.” Revenge, however, may serve as either a verb or noun, and is appropriate in this usage.

hey, revenge may be used as a noun. But here, it is being used as a verb. Maybe it isn’t the verb phrase of the sentence, but it is a verb in this case.

A noun usage would read something like, “It shall be a revenge!” Or better, “Our revenge shall be sweet!”