
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 $S\_n$, and it is known that $S\_n=2^{n+1}-n-2 (n \in \mathbb{N}^*)$.
(I) Find the general term formula of the sequence $\{a\_n\}$;
(II) If $b_n= \frac{n}{a_{n+1}-a_{n}}$, find the sum of the first $n$ terms of the sequence $\{b\_n\}$, denoted as $T\_n$.

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