BALKAN-SL 2012 A6

Let $k$ be a positive integer. Find the maximum value of $$a^{3k-1}b+b^{3k-1}c+c^{3k-1}a+k^2a^kb^kc^k,$$ where $a$, $b$, $c$ are non-negative reals such that $a+b+c=3k$.