21 In a regular tetrahedron wooden block $ABCD$ with edge length 2, there is a point $P (AP<1)$ on the edge $AB$. A cross-section perpendicular to the edge $AB$ is to be sawed through point $P$. When the sawing stops at a certain position, it is measured that the saw cut $PM=1$ on the face $ABD$. The saw cut $PN=\frac{2}{3}$ on the face $ABC$, then $MN=$