Second:
It seems you may be viewing this fatalisticlly. By fatalism I mean the idea that the ends is accomplished with no reference to the means.
What I mean is, you seem to think that predestination means that some people are saved regardless of whether or not they come to faith in Christ via the gospel message.
That's not what it means.
So in a sense, it is
not true that "nothing you do will affect your salvation". If one never comes to faith in Christ, he is not saved.
What predestination teaches is that God has an ends, but he uses means to accomplish that ends. We read in many verses, such as Acts 13:48, that sinners believe because they are appointed to eternal life.
So you see, they do believe. They believe willingly and freely. But the reason for it is because of God's predestination grace. No where does the Bible say that people are just saved regardless of what they do during their life.
Predestination by itself saves nobody - rather, it marks people out who will respond positively to the gospel.
Ends, and the means to the end. Through evangelism God visits sinners with his grace and changes our hearts, removes our blindfolds, and effectually brings us to Christ.
In short, we are unwilling by fallen nature, due to corruption of sin, but by God's grace we become willing.
"I will remove your heart of stone and give you a heart of flesh, and cause you to obey my statutes".
"Your people will be willing in the day of your power"
"He caused us to be born again.."
"It is God's doing that you are in Christ Jesus".
Surely these Bible verses are popping up in your mind