Let $ABC$ be a triangle, and $P$ be a variable point inside $ABC$ such that $AP$ and $CP$ intersect sides $BC$ and $AB$ at $D$ and $E$ respectively, and the area of the triangle $APC$ is equal to the area of quadrilateral $BDPE$. Prove that the circumscribed circumference of triangle $BDE$ passes through a fixed point different from $B$.