What interacts correctly with the negation expressed in the context given?

The choice that interacts correctly with the negation in the context provided is "Neither do I." This phrase is used to express agreement with a negative statement made by someone else. It follows the structure required for such constructions in English, effectively indicating that the speaker shares the same negative sentiment.

In English, when you use "neither," it is typically followed by an inverted auxiliary verb and the subject. The phrase "Neither do I" conforms to this structure, where "do" serves as the auxiliary verb, and "I" is the subject. This ensures that the response maintains parallelism with the negative statement that precedes it.

The other options do not maintain the correct grammatical structure necessary to properly express agreement with a negative statement. For example, "Neither me" lacks the verb component and doesn't form a complete thought, while "Neither I do" breaks the proper order of subject and auxiliary verb. "Neither he does" also misaligns as it does not correspond accurately to the inversion required in this context. Thus, "Neither do I" effectively fulfills the grammatical requirement of the interaction in a negative context.