Think deeply (8)
'think deeply' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for cogitate that I've seen before include "Think deeply, ponder" , "Use little grey cells" , "Get to CIA in order to think deeply" , "Meditate - reflect" , "Do some thinking" .)
(Other definitions for muse that I've seen before include "Be absorbed in thought" , "Contemplate -- a goddess of the liberal arts" , "Contemplation" , "Inspiring goddess" , "Goddess; rock group" .)