
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given a sequence $\{a_n\}$ that 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:

(1) Find the value of $q$ and the general formula for $\{a_n\}$;  
(2) 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 $\{b_n\}$.

Present the answer in LaTex format: \boxed{Your answer}
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