
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 sum of the first $n$ terms denoted as $S_n$, and $S_{n} = 2a_{n} - 2$ where $n \in \mathbb{N}^{*}$.  
(1) Find the general term $a_n$ of the sequence $\{a_n\}$.  
(2) Let $c_n = (n+1)a_n$, find the sum of the first $n$ terms $T_n$ of the sequence $\{c_n\}$.

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