
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
In the geometric sequence $\{a_n\}$, $a_2=3$, $a_5=81$.

(1) Find the general formula for $\{a_n\}$.

(2) Let $b_n=\log_3{a_n}+1$, calculate the sum of the first $n$ terms, $T_n$, of the sequence $\left\{\frac{1}{b_nb_{n+1}}\right\}$.

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