Let ABC be an isosceles triangle with sides AB = AC = 13 and BC = 10. Let points D and E lie on segments BC and AC respectively, so that the path from A to D to E to F, with point F being on side AB such that AF= 3, is minimized. Find the length of this minimum path rounded to its nearest integer. (btw calculators are allowed on this problem, but it is not necessary for solving)