"Write with a pen" is not an adverbial, but a conjunction. The first basis for judging adverbials is part of speech. Most adverbials can be time nouns, will verbs, adjectives, prepositional phrases, quantifier phrases and other phrases. The second is meaning. Adverbials are restrictive or descriptive in meaning. Verbs used as adverbials are generally auxiliary verbs and will verbs. Conjunction phrases are indistinguishable from (verb+noun)+background+predicate. Mainly depends on whether the preceding verb has lost its "action". I love to go, I can go, I {should go by car with me, I'll take a taxi-different. I'm going to work soon, which is different from going to Beijing by car. As the adverbial is an additional component, it can be removed. I go to work.-I work, yes. I go to Beijing by car, but I can't do without going. 1