Why is the distance function pluri-subharmonic?

Question

Let $(X,J,\omega)$ be an almost-Kähler manifold with contact-type boundary $\partial X$, which is $J$-convex, then why is the function $\psi (x):=\mathrm{dist} (x,\partial X)^2$ a plurisubharmonic function on $X$? Here contact-type boundary means that there is a contact form $\lambda$ defined on $\partial X$ such that $\omega\vert_{\partial X} =\mathrm{d}\lambda$ and $\xi =\ker\lambda$ is the tangent distribution of $\partial X$, and the orientation of $\partial X$ as a boundary of $X$ coincides with the orientation defined by $\lambda\wedge (\mathrm{d}\lambda )^{n-1}$. It is $J$-convex if $\mathrm{d}\lambda$ is positive definite on $\xi$.