
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 it satisfies $S\_n=2-a\_n$, for $n=1$, $2$, $3$, $...$.
(1) Find the general term formula for the sequence $\{a\_n\}$;
(2) If sequence $\{b\_n\}$ satisfies $b\_1=1$, and $b_{n+1}=b\_n+a\_n$, find the general term formula for the sequence $\{b\_n\}$;
(3) If $c\_n=n(3-b\_n)$, find the sum of the first $n$ terms for the sequence $\{c\_n\}$, denoted as $T\_n$.

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