grammatical number - Are two singular nouns together singular or plural?

I'm writing a research paper with several classmates for school. However, there's a sentence that we, as well as others who have reviewed our paper, disagree with on how to write. Which sentence is more proper, grammatically?

Yet, alcohol usage and abuse still continue.

Yet, alcohol usage and abuse still continues.

I realize that this is probably a trivial question, but I would appreciate any help nonetheless.

Answer

My impression is that alcohol use and alcohol abuse are overlapping but hardly coextensive entities. Consequently I would revise your sentence to say something along the lines of

Yet alcohol use and abuse remain extremely common.

In making this recommendation, I don't deny that cases may arise in which a singular verb works better than a plural verb with a subject that looks plural but is understood as a unitary thing. For example,

Cutting and pasting in Word is a simple procedure.

sounds far better to me than either

Cutting and pasting in Word are a simple procedure.

or

Cutting and pasting in Word are simple procedures.

because I understand cutting and pasting to be two parts of a single procedure in Word, not two separate procedures that often occur in tandem.