Yes, you can (and should!) use action verbs in your cover letter.
Using action verbs in your cover letter makes your writing more engaging and impactful. Aside from making your vocabulary more varied and interesting, action verbs tell the reader how you achieved something.
Because action verbs are more descriptive, they're ideal for highlighting your expertise on your cover letter:
PolySpeak needs interpreters who are able to think quickly and adapt to different contexts and registers. As a freelance interpreter for Face-to-Face, I accompanied clients from various backgrounds to medical appointments, adapting my communication style to reflect specific needs and cultural taboos.
The action verbs 'accompanied' and 'adapting' tells us what kind of professional relationship the applicant had with their clients, and highlights valuable soft skills like empathy and customer service.