Let $A$, $B$, and $C$ be three events in a sample space. You are given that $P(A) = 0.5$, $P(B) = 0.4$, and $P(C) = 0.3$. Furthermore, $A$ and $B$ are independent, and $B$ and $C$ are mutually exclusive. Determine the minimum possible value of $P(A \cup B \cup C)$.