2014 KIMC keystage3-IWYMIC individual Question 5

In triangle $ABC$, $\angle CAB=\angle BCA=45^\circ$. $L$ is the midpoint of $BC$ and $P$ is a point on $CA$ such that $BP$ is perpendicular to $AL$. If $CP=\sqrt2$ cm, what is the length, in cm, of $AB$?