
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
Determine $S_n$, the sum of the first $n$ terms of a sequence where the first term is $2$, and each subsequent term grows by an increasing number that is a multiple of 3. More specifically, the difference between consecutive terms begins at 3 and increases by 3 for each new term.
A) $\frac{n(n+1)(n+1)}{4} + 2n$
B) $\frac{n(n+1)(2n+1)}{6} + 2n$
C) $1.5n^2 - 1.5n + 2n$
D) $\frac{n(n+1)}{2} + n$

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