
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
An exponential sequence $\left\{a_{n}\right\}$ consists of positive terms, and $2a_{1}+3a_{2}=1$, $a_{3}^{2}=9a_{2}a_{6}$.

(1) Find the general formula for the sequence $\left\{a_{n}\right\}$;

(2) Let $b_{n}=\log _{3}a_{1}+\log _{3}a_{2}+\ldots +\log _{3}a_{n}$. Find the sum of the first $n$ terms of the sequence $\left\{\dfrac{1}{b_{n}}\right}$.

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