
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
Let the sum of the first $n$ terms of the sequence $\{a_n\}$ be $s_n=\frac{3^{n+1}-3}{2}$, and the sequence $\{b_n\}$ satisfies $b_n=\frac{1}{(n+1)\log_3{a_n}}$.  
(1) Find the general formula for the sequence $\{a_n\}$.  
(2) Find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $B_n$.

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