
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 its first $n$ terms sum $S\_n$, and $(S\_n-1)^{2}=a\_nS\_n (n∈N^{})$.
(1) Find the values of $S\_1$, $S\_2$, $S\_3$;
(2) Find the general formula for $S\_n$ and the sequence $\{a\_n\}$;
(3) Given $b\_n=(-1)^{n-1}(n+1)^{2}a\_n a_{n+1} (n∈N^{})$, 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}
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