Real function

You are given that $a,b$ and $c$ are positive real numbers satisfying $a+b+c\leq \frac{3}{2}$ . Let $P$ is the minimum value of the expression below.

$\sum_{\text{cyclic}} \sqrt{2a^2+\frac{1}{a^2b^2}+\frac{2}{b}}$ Find $\left \lfloor 1000P \right \rfloor$