
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 sequences $\{a_n\}$, $\{b_n\}$, and $S_n$ as the sum of the first $n$ terms of $\{a_n\}$, satisfying $S_{n+1}=S_{n}+a_{n}+2n+2$. If $a_{1}=b_{1}=2$, $b_{n+1}=2b_{n}+1$, where $n\in\mathbb{N}^*$.  
(I) Find the general formula for sequences $\{a_n\}$ and $\{b_n\}$.  
(II) Let $c_{n}= \frac {3a_{n}}{n(b_{n}+1)}$, find the sum of the first $n$ terms of sequence $\{c_{n}\}$, denoted as $T_{n}$.

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