
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 positive geometric sequence $\{a\_n\}$ that satisfies $a\_4 = a\_2a\_3$, and the sum of the first three terms $S\_3 = 13$.
(1) Find $a\_n$;
(2) If sequence $\{b\_n\}$ satisfies $b\_n = \log\_3 a\_n + n$, find the sum of the first $n$ terms, $T\_n$, of the sequence $\{\frac{1}{b\_n b\_{n+1}}\}$.

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