
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 $\{an\}$ with the sum of its first $N$ terms denoted as $sn$. The first term is $a\_1=1$, and it satisfies the equation $2S\_n=(n+1)a\_n$.

(I) Find the general formula for the $n$-th term of the sequence.
(II) Find the sum $T\_n$ of the first $n$ terms of the sequence $\{\frac{1}{a\_na\_{n+2}}\}$.

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