Many people are uncomfortable with grammar because they've been frustrated by it in the past, and not without good reason, too, given the number of rules, their complexity, and all the terminology necessary even to understand them. To complicate, there are probably more exceptions to rules than there are rules. Comfort with the rules of grammar will make you a more fluent, confident writer, however. If reading a rule doesn't help you understand it, remember it, or figure out when it applies, you may find it more useful to study the example and come up with your own guidelines.
Verbs always agree with their subjects, even when the subjects are far away.
The second entry in this long list of books and articles interests me most. Expressions like as well as, in addition to, accompanied by, together with, and along with do not affect subject-verb agreement. This book , together with the related articles, clarifies the situation for me. Professor Meyers and her assistant have completed their groundbreaking work. Lists preceded by each and every take singular verbs.