Square $ABCD$ has sides of length $6$. Points $P$ and $Q$ lie on $\overline{AD}$ and $\overline{CD}$, respectively, with $AP=3$ and $DQ=\frac{18}5$. A path begins along the segment from $P$ to $Q$ and continues by reflecting against the sides of $ABCD$ (with congruent incoming and outgoing angles). If the path hits a vertex of the square, it terminates there; otherwise it continues forever. At which vertex does the path terminate? (Answer with $A$, $B$, $C$, $D$, or say that the path continues forever.)
$\textbf{(A) } A \qquad$ $ \textbf{(B) } B \qquad$ $ \textbf{(C) } C \qquad$ $ \textbf{(D) } D \qquad$ $ \textbf{(E) } \text{The path continues forever.}$ 