
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
The terms of the geometric sequence $\{a_n\}$ are all positive, and $2a_1 + 3a_2 = 1$, $a_3^2 = 9a_2a_6$.
(1) Find the general term formula of the sequence $\{a_n\}$;
(2) Let $b_n = \log_3{a_1} + \log_3{a_2} + \dots + \log_3{a_n}$, find the sum of the first $n$ terms $T_n$ of the sequence $\{ \frac{1}{b_n} \}$.

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