ISL 2020 A4

Let $a, b, c, d$ be four real numbers such that $a \geqslant b \geqslant c \geqslant d>0$ and $a+b+c+d=1$. Prove that $$(a+2 b+3 c+4 d) a^{a} b^{b} c^{c} d^{d}<1$$ (Belgium)