
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 sum of the first $n$ terms of the sequence $\{a\_n\}$ is $S\_n= \frac {3^{n+1}-3}{2}$, and the sequences $\{b\_n\}$ and $\{c\_n\}$ are defined by $b\_n= \frac {1}{(n+1)\log _{3}a\_n}$ and $c\_n=(2n+1)a\_n$ respectively.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Find the sum of the first $n$ terms of the sequence $\{b\_n\}$, denoted as $B\_n$.
3. Find the sum of the first $n$ terms of the sequence $\{c\_n\}$, denoted as $C\_n$.

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