
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 its first $n$ terms denoted as $S_n$. It is known that $S_n = 2a_n - 3n, (n \in \mathbb{N^+})$.

(1) Find the values of $a_1$, $a_2$, and $a_3$.
(2) Determine if there exists a constant $\lambda$ such that ${a_n + \lambda}$ forms a geometric sequence. If it exists, find the value of $\lambda$ and the general term formula $a_n$. If not, explain the reason.

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