
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
Consider a geometric sequence $\\{a_n\\}$ where all terms are positive numbers, and $2a_1 + 3a_2 = 1, a_3^2 = 9a_2a_6$.

(1) Find the expression for $a_n$.
(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 of the sequence $\\{ \frac{1}{b_n} \\}$.

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