In the film Good Will Hunting, what are the two turning points for the main character? What is the symbol in the film and its significance to the characters?

Good Will Hunting is a 1997 American drama film starring the late Robin Williams, Ben Affleck, and Matt Damon. The film won two Academy Awards: one for Best Original Screenplay, awarded to Matt Damon and Ben Affleck; and one for Best Actor in a Supporting Role, awarded to Robin Williams. The story follows a young man named Will Hunting (Matt Damon) who works as a janitor at MIT and proves his ability to solve difficult math formulas that not many people in the world can solve; he is actually a genius. He grew up as an orphan and has difficulty connecting with people, which is why he only has three friends. After assaulting a police officer, Will is arrested and meets Dr. Sean Maguire, who is a psychologist and becomes his therapist. He also becomes his close friend and advisor, encouraging Will to think upon his life choices and reevaluate his relationships with his friends and girlfriend. Coincidently, Dr. Maguire was also a victim of child abuse and helps Will break out of his shell and deal with his dark past. Meeting Dr. Maguire is definitely the most important turning point in Will's life.
Will begins to study advanced mathematics with a world-renowned professor as people start to appreciate and admire his genius. At the same time, Will also pursues a relationship with a girl named Skylar. I believe the second major turning point in Will's life is his breakup with Skylar; Skylar asks Will to come with her to California, and Will isn't sure that this is the right choice for him. They argue and say things to each other that they might regret later. Skylar beings to doubt that Will loves her, and, in the end, he says that he doesn't. Thus, they put an end to their relationship. I believe the fight and the breakup with his girlfriend greatly contributed to Will's character development, because they helped him realize that love and happiness are the most important things in life. This is why, in the end, he drives to California to reunite with Skylar.
One of the more important symbols in the film is probably the painting that Dr. Maguire painted. When Will first sees it he criticizes it, but the more he stares at the painting, the more he realizes that it actually represents Dr. Maguire's life. Will uses the painting to psychoanalyze Dr. Maguire, but the doctor turns the tables and uses the painting to psychoanalyze Will, thus helping him understand his character flaws.