Let $A, B,$ and $C$ be events in a sample space $S$ such that $P(A) = 0.4, P(B) = 0.3,$ and $P(C) = 0.2$. If $A$ and $B$ are independent, $B$ and $C$ are mutually exclusive, and $A$ and $C$ are independent, calculate $P(A \cup B \cup C)$ given $P(A \cap B \cap C) = 0.01$.