Question 36
Suppose that $a, b, c$, and $d$ are real numbers such that $a+b+c+d=8$. Compute the minimum possible value of
$$
20\left(a^{2}+b^{2}+c^{2}+d^{2}\right)-\sum_{\text{sym}} a^{3} b,
$$
where the sum is over all 12 symmetric terms.
$$
20\left(a^{2}+b^{2}+c^{2}+d^{2}\right)-\sum_{\text{sym}} a^{3} b,
$$
where the sum is over all 12 symmetric terms.