
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 $S\_n=3n^{2}+8n$, and $\{b\_n\}$ is an arithmetic sequence where $a\_n = b\_n + b_{n+1}$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Find the general term formula for the sequence $\{b\_n\}$.
3. Let $c_{n}= \frac {(a_{n}+1)^{n+1}}{(b_{n}+2)^{n}}$, find the sum of the first $n$ terms of the sequence $\{c\_n\}$, denoted as $T_n$.

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