
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 a sequence $\{a_n\}$ with the sum of its first $n$ terms $S_n = 3n^2 + 8n$, and $\{b_n\}$ is an arithmetic sequence, and $a_n = b_n + b_{n+1}$.  
(Ⅰ) Find the general formula for the sequence $\{b_n\}$.  
(Ⅱ) Let $c_n = \dfrac{(a_n + 1)^{n+1}}{(b_n + 2)^n}$, find the sum of the first $n$ terms of the sequence $\{c_n\}$, $T_n$.

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