
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 ${a_n}$ with the first term $a_1=1$, the sum of the first $n$ terms is $S_n$, and it satisfies $(n+1)a_n=2S_n (n\in\mathbb{N}^*)$.

(I) Find the general term formula for the sequence ${a_n}$.

(II) Let $b_n=a_n\cos (\pi a_n)$, find the sum of the first $n$ terms, $T_n$, for the sequence ${b_n}$.

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