
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 an geometric sequence $\{a\_n\}$ where all terms are positive, and $a\_1 + 2a\_2 = 1$, and $a\_3^2 = 4a\_2 \cdot a\_6$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Let $b\_n = \log\_2 a\_1 + \log\_2 a\_2 + \log\_2 a\_3 + \ldots + \log\_2 a\_n$, find the sum of the first $n$ terms of the sequence $\{\frac{1}{b\_n}\}$.
3. Let $c\_n = \frac{b\_n \cdot a\_n}{n}$, find the sum of the first $n$ terms of the sequence $\{c\_n\}$.

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