Question 24
Find the smallest real number $M$ such that there exist complex numbers $a, b, c, d$ with $|a| = |b| = |c| = |d| = 1$ satisfying: for any complex number $z$ with $|z| = 1$,
$$
|az^3 + bz^2 + cz + d| \le M.
$$
$$
|az^3 + bz^2 + cz + d| \le M.
$$