BRILLIAthon $2$ (Problem $3$ )

The real numbers $a, b, c, d$ are such that

$a \geq b \geq c \geq d > 0$

and

$a + b + c + d = 1$

Is the following mathematical statement true?:

$(a + 2b + 3c + 4d) a^a b^b c^c d^d < 1$

Source: International Mathematical Olympiad $2020$ , Day $1$ , Problem $2$