BALTIC-WAY 2018 Problem 3

Let $a, b, c, d$ be positive real numbers such that $a b c d=1$. Prove the inequality

$$\frac{1}{\sqrt{a+2 b+3 c+10}}+\frac{1}{\sqrt{b+2 c+3 d+10}}+\frac{1}{\sqrt{c+2 d+3 a+10}}+\frac{1}{\sqrt{d+2 a+3 b+10}} \leq 1 .$$