Let $A$ and $B$ be two events such that $P(A) = 0.3$, $P(B) = 0.4$, and $P(A|B) = 0.2$. If $C$ is an event such that $P(C) = 0.5$ and $C$ is independent of both $A$ and $B$, what is $P(A \cup B \cup C)$?