In a parallel-series routing network, current can flow from the input to the output if either Path 1 is active or Path 2 is active. Path 1 consists of two independent switches $A$ and $B$ connected in series (both must be closed for Path 1 to be active). Path 2 consists of a single switch $C$ (which must be closed for Path 2 to be active). If each switch is closed independently with probability $0.6$, what is the probability that current can flow from the input to the output?