Given the sequence $\{a_n\}$ satisfies $a_{n+2} = qa_n$ (where q is a real number and $q \neq 1$), $n \in \mathbb{N}^*$, $a_1 = 1$, $a_2 = 2$, and $a_2 + a_3$, $a_3 + a_4$, $a_4 + a_5$ form an arithmetic sequence.
(I) Find the value of q and the general term formula of $\{a_n\}$;
(II) Let $b_n = \frac{\log_2 a_{2n}}{a_{2n-1}}$, $n \in \mathbb{N}^*$. Find the sum of the first n terms of the sequence $\{b_n\}$.