
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 $\{a_n\}$, the sum of its first $n$ terms is $S_n$, and it satisfies $S_n = 2 - a_n$ for $n=1, 2, 3, \ldots$.
1. Find the general term formula for the sequence $\{a_n\}$.
2. If the 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. Let $c_n = n(3 - b_n)$, find the sum of the first $n$ terms of the sequence $\{c_n\}$, denoted as $T_n$.

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