Here's my take as a Calvinist...(had to get that in there!)
Justification is monergistic. We do nothing to be saved. Even the repentance and faith that we exercise is a gift from God.
BUT, sanctification is synergistic. We have certain things to do - in this passage, obedience. We have to do that. We have to persevere or we are not finally saved. This is the only way to make sense of the warning in this passage (fear and trembling) and the other passages written to those who claim to be saved.
The way I ended that last sentence is very important. Not everyone who claims to be saved is saved. The local church is full of tares as well as wheat. Those who claim to be saved, yet to not have fruit, are not really saved, and will be burned.
Those who are saved have God working in them both to desire (will) good works and to do them. So, on one hand, we are responsible for it. But on the other hand, God does it.
Those who are truly saved will have good works at the judgment because they are "wrought in God." Those who are unsaved, no matter what their claim, will have bad works at the judgment. This is why the Bible says that salvation (justification) is by faith, but final judgment is by works.
Glorification is monergistic. There is nothing we do (except maybe die) that has anything to do with this. It is all a work of God.
Those who God begins the work of salvation in unfailingly make it to the end. In the meantime, we are to work out our own salvation, and thus, "make our call and election sure." (2 Peter 1:10)