A point $P$ lies inside $\vartriangle ABC$ such that the values of areas of $\vartriangle PAB, \vartriangle PBC, \vartriangle PCA$ can form a triangle. Let $BC = a,CA = b,AB = c, PA = x,PB = y, PC = z$, prove that $$\frac{(x + y)^2 + (y + z)^2 + (z + x)^2}{x + y + z} \le a + b + c$$