
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 the first $n$ terms $S_n = 3n^2 + 10n$, and $\{b_n\}$ is an arithmetic sequence, also given that $a_n = b_n + b_{n+1}$,

(Ⅰ) Find the general term formula for the sequence $\{b_n\}$;  
(Ⅱ) Let $c_n= \frac {(a_{n}+1)^{n+1}}{(b_{n}+2)^{n}}$, find the sum of the first $n$ terms $T_n$ for the sequence $\{c_n\}$.

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