
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
In the geometric sequence $\\{a_n\\}$, $(a_2 - a_1 = 2)$, and $(2a_2)$ is the arithmetic mean of $(3a_1)$ and $(a_3)$.

(I) Find the first term and common ratio of the sequence $\\{a_n\\}$.

(II) Find the sum of the first $n$ terms of the sequence $\\{a_n\\}$, denoted as $S_n$.

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