Which of the following does NOT correctly utilize a correlative conjunction?

The choice that does not correctly utilize a correlative conjunction is indeed the one that includes the phrase "however go out." Correlative conjunctions are pairs of conjunctions that work together to join words or groups of words, creating a balanced relationship between the elements they connect.

In the context provided, a proper correlative conjunction would be a pair such as "either...or," "neither...nor," or "both...and." The phrase in question attempts to use "however" in a manner that doesn't create this balanced relationship. Instead, "however" functions as a conjunctive adverb, which does not fit the requirement for a correlative construction.

In contrast, the other options properly use correlative conjunctions. The first option illustrates "not only...but also," indicating that two related ideas are presented. The second option uses "either...or," effectively showing a choice between two outcomes. The third option, although a bit awkward (both...and typically pairs nouns or phrases), does correctly relate a pairing of two actions connected by the conjunctions of "both" and "and."

Thus, the correct choice highlights a misuse of conjunctions that fails to establish the intended relationship between the two clauses in the sentence.