IR-TST 2015 Problem 12

If $a,b,c$ are positive real numbers such that $a+b+c=abc$ prove that $$\frac{abc}{3\sqrt{2}}\left ( \sum_{cyc}\frac{\sqrt{a^3+b^3}}{ab+1} \right )\geq \sum_{cyc}\frac{a}{a^2+1}$$