
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 $S_n$ as the sum of the first $n$ terms of the sequence $\{a_n\}$, and it satisfies $S_n = 2a_n - 2$ for $n \in \mathbb{N}^{*}$.
(1) Find the general formula for the sequence $\{a_n\}$.
(2) In triangle $\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are 3, $a_1$, and $a_2$ respectively. Calculate the area of $\triangle ABC$.

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