Hi Jeff,
this question is truly wonderful as it tests both your vocabulary and grammar
The key to solving it is to read the question very very carefully.
It gives to clues , Firstly the gramatically clue nevertheless.
The adverbial phrase "nevertheless" is used to join two clauses with a contradictory opinon.
There are two such words for which you might have to find the antonym - free and introspective .
Also note that the adverb paradoxically points out that rather than going for introspective you should look for an antonym for free because free is also preceded by an adverb. The only antonym which fits in would be controlled.
The rest of the word dont actually contradict and sever as antonyms for the word free.
Hope this answer is somewhat convincing. :-)
Regards
Aster