
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 $a\_1+2a\_2=1$, $a\_3^2=4a\_2a\_6$.
(1) Find the general term formula of the sequence;
(2) Let $b\_n=\log\_2a\_1+\log\_2a\_2+...+\log\_2a\_n$, find the sum of the first $n$ terms of the sequence $\{ \frac{1}{b\_n}\}$.

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