6. Real numbers $a, b, c, d$ satisfy the equation $a b + b c + c d + d a = 16$.

a) Prove that among the numbers $a, b, c, d$, there are two with a sum of at most 4.

b) What is the minimum value that the sum $a^{2} + b^{2} + c^{2} + d^{2}$ can have?