Acutely, intensely (6)
I believe the answer is:
keenly
I believe this clue is a double definition.
'acutely' is the first definition.
(I know that acutely can be written as keenly)
'intensely' is the second definition.
(thesaurus)
(Other definitions for keenly that I've seen before include "With eagerness" , "Eagerly, enthusiastically" , "In an eager manner" , "With enthusiasm" , "Eagerly, sharply" .)