Too many lines

In a triangle $ABC$ , $AD$ is a median. $E$ is the midpoint of $BD$ . Segment $CF$ is drawn through $P$ , the midpoint of $AD$ , with $F$ on $AB$ . $DG$ is drawn parallel to $CF$ with $G$ on $AB$ . $AE$ cuts $DG$ at $H$ . Find the ratio of the area of triangle $ADH$ to the area of triangle $ABC$ . Give answer in decimals.