
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
Let the sequence $\{a_n\}$ have a sum of the first $n$ terms denoted by $S_n$. If for any $n \in \mathbb{N}^*$, it holds that $S_n = 2a_n - 3n$.

    (1) Find the first term and the recursive relation $a_{n+1} = f(a_n)$ of the sequence $\{a_n\}$;

    (2) Read the following theorem first: If a sequence $\{a_n\}$ has a recursive relation $a_{n+1} = Aa_n + B$, where $A$ and $B$ are constants, and $A \neq 1$, $B \neq 0$, then the sequence $\left\{a_n - \frac{B}{1-A}\right\}$ forms a geometric sequence with a common ratio of $A$. Based on the solution to question (1), apply this theorem to find the general formula for the sequence $\{a_n\}$;

    (3) Find the sum of the first $n$ terms $S_n$ of the sequence $\{a_n\}$.

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