A parallelogram ABCD with ∣AD∣=∣BD∣ has been given. A point E lies on line segment ∣BD∣ in such a way that ∣AE∣=∣DE∣. The (extended) line AE intersects line segment BC in F. Line DF is the angle bisector of angle CDE. Determine the size of angle ABD.
[asy]
unitsize (3 cm);pair A, B, C, D, E, F;D = (0,0);
A = dir(250);
B = dir(290);
C = B + D - A;
E = extension((A + D)/2, (A + D)/2 + rotate(90)*(A - D), B, D);
F = extension(A, E, B, C);draw(A--B--C--D--cycle);
draw(A--F--D--B);dot("A", A, SW);
dot("B", B, SE);
dot("C", C, NE);
dot("D", D, NW);
dot("E", E, S);
dot("F", F, SE);
[/asy] geometryparallelogramanglesequal segments