Let $D$ be a point inside $\triangle ABC$ such that $\angle CDA + \angle CBA = 180^{\circ}.$ The line $CD$ meets the circle $\odot ABC$ at the point $E$ for the second time. Let $G$ be the common point of the circle centered at $C$ with radius $CD$ and the arc $\overset{\LARGE \frown}{AC}$ of $\odot ABC$ which does not contain the point $B$. The circle centered at $A$ with radius $AD$ meets $\odot BCD$ for the second time at $F$. Prove that the lines $GE, FD, CB$ are concurrent or parallel.