In the figure below, $D$ is a point on segment $\overline{CE}$ such that $\overline{AD}\parallel\overline{BE }$ and $A$ is not on $\overline{BC}.$ Line segments $\overline{AD}$ and $\overline{BC}$ intersect at $P.$ [asy] size(4cm); pair C = (0,0); pair D = (4,0); pair E = (9,0); pair F = (0.25,4); pair G = (1,4); pair A = extension(C, F,D, G); pair H = G+E-D; pair B = extension(C, G,E, H); pair P = extension(A, D,B, C); draw(A--C--E--B--C); draw(A--D); label("$A$",A, NNW); label("$B$",B, N); label("$C$",C, SSW); label("$D$",D, S); label("$E$",E, SSE); label("$P$",P, dir(0)); [/asy]

Can $\angle CAD=\angle CBE?$ Explain.