You will be amazed with this

Algebra Level 5

$\begin{cases} a&+&b&+&c&+&d&+&e&=&8 \\ a^2&+&b^2&+&c^2&+&d^2&+&e^2&=&16 \\ \end{cases}$

Given that the real numbers $a, b, c, d, e$ satisfy the system of equations above, find the sum of the maximum and minimum possible value of $a$ .