
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
Given that the sequence $\{a_n\}$ is a geometric sequence, with $a_1=3, a_4=81$, if the sequence $\{b_n\}$ satisfies $b_n=(n+1)\log_3{a_n}$, then the sum of the first $n$ terms of $\left\{ \frac{1}{b_n} \right\}$, $S_n=$ .

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