JBMO-SL 2019 A6

Let $a, b, c$ be positive real numbers. Prove the inequality

$$\left(a^{2}+a c+c^{2}\right)\left(\frac{1}{a+b+c}+\frac{1}{a+c}\right)+b^{2}\left(\frac{1}{b+c}+\frac{1}{a+b}\right)>a+b+c$$