The function $f(x) = a\cos bx + 3$ is defined on the closed interval $[0, 2\pi]$ and has a maximum value of 13 at $x = \frac{\pi}{3}$. For the ordered pair $(a, b)$ of two natural numbers $a$ and $b$ satisfying this condition, what is the minimum value of $a + b$? [4 points]\\
(1) 12\\
(2) 14\\
(3) 16\\
(4) 18\\
(5) 20