
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 satisfies $2S_n=n-n^2 (n \in \mathbb{N}^*)$.
(I) Find the general term formula of the sequence ${a_n}$;
(II) Let $b_n = \begin{cases} 2^{a_n} & (n=2k-1) \\ \frac{2}{(1-a_n)(1-a_{n+2})} & (n=2k) \end{cases} (k \in \mathbb{N}^*)$, 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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