The word that should be used to complete the blank shown above is "independently."
We can reach this conclusion because:
The blank should be filled with a variation of the word "depend" as shown in the question.
This word should promote coherence and cohesion to the sentence.
The word must also cooperate with the meaning expressed in the sentence.
The word that meets all of these requirements is the word "independently," because, in addition to being a meaningful word that cooperates with the message that the sentence is intended to convey, it is coherent and linked to the word "depend."
