
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 sequence $\{a\_n\}(n\in N^{*})$, the sum of the first $n$ terms is $S\_n$, which satisfies $2S\_n=n-n^{2}$.
(I) Find the general term formula of the sequence $\{a\_n\}$;
(II) Let $b\_n= \begin{cases} n\cdot 2^{a\_n},n=2k-1 \\\\ \frac {1}{n^{2}+2n},n=2k\end{cases}(k$ is a positive integer$)$, find the sum of the first $2n$ terms of the sequence $\{b\_n\}$, denoted as $T\_{2n}$.

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