A term that describes an action that increases annoyance is:

The term that accurately describes an action that increases annoyance is "exasperate." This word specifically refers to a state of irritation or frustration that is heightened by repeated actions or behaviors. When someone exasperates another, they are provoking a sense of annoyance or aggravation, often through relentless or bothersome actions.

In contrast, "enumerate" means to list items or count them individually, which does not imply any emotional response. "Euphemism" is a linguistic term that refers to a mild or indirect word or expression used in place of one that may be considered harsh or blunt, and it also does not relate to annoyance. "Exacerbate," while relevant in the realm of intensifying a negative situation, is broader and might refer to worsening conditions or problems in general rather than specifically increasing annoyance. Therefore, "exasperate" is the most precise choice when defining an action that specifically heightens annoyance.