PAMO 2024 Problem 2

In triangle $ABC$ ,let $M$ be the midpoint of the side $BC$ ,and $N$ is the midpoint of the segment $AM$ ,the circle going through $N$ and tangent the line $AC$ at $A$ intersects the segment $AB$ again in $P$ .

prove that the circumcircle of triangle $BPM$ is tangent the line $AM$