
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 $\left\{a_{n}\right\}$ with positive terms, such that $2a_{1}+3a_{2}=1$ and $\left(a_{3}\right)^{2}=9a_{2}a_{6}$.

(1) Find the general term $\left(a_{n} \right)$;

(2) Let $b_{n}=\log_{3}{a_{1}}+\log_{3}{a_{2}}+\cdots+\log_{3}{a_{n}}$, find the sum of the first $n$ terms of the sequence $\left\{\frac{1}{b_{n}}\right\}$ denoted as $T_{n}$.

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