An electrical safety system contains three independent relays, $X$, $Y$, and $Z$, with success probabilities $P(X) = 0.8$, $P(Y) = 0.7$, and $P(Z) = 0.6$. The system succeeds if at least two relays function properly, with the strict condition that if relay $X$ fails, the entire system fails immediately. Determine the probability that the system functions successfully.