
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
In the arithmetic sequence $\{a\_n\}$, $a\_1=1$, and the sum of the first $n$ terms, $S\_n$, satisfies the condition $\frac{S_{2n}}{S\_n}=\frac{4n+2}{n+1},n=1,2,...$.
(I) Find the general term formula of the sequence $\{a\_n\}$;
(II) Let $b\_n=a\_np^{a\_n}(p > 0)$, 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}
user