Let $p$, $q$ and $r$ be real numbers with $p^2 + q^2 + r^2 = 1$.\\
(a) Prove the inequality $3p^2 q + 3p^2 r + 2q^3 + 2r^3 \leq 2$.\\
(b) Also find the smallest possible value of $3p^2 q + 3p^2 r + 2q^3 + 2r^3$. Specify exactly when the smallest and the largest possible value is achieved.