well, keen itself means smart or sharp. Keenly is a verb which means, " to perform an action sharply,precisely or with accuracy". :)
It is an action verb.
The word sharply modifies an action to indicate it is done in a sharp (or precise) manner.
began is an action verb, not a linking verb.
action verb because you did this action (sent)
what follows a linking or action verb
Action verb
It is an action verb.
action verb
Action verb
An action verb
The verb stay is an action verb.