
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
The sum of the first $n$ terms of the sequence $\{a_{n}\}$ is $S_{n}=n^{2}+3n+2$. Find the general term formula for $\{a_{n}\}$.

A) $a_{n}=2n-2$
B) $a_{n}=2n+2$
C) $a_{n}=\begin{cases} 6,n=1 \\\\ 2n-2,n\geqslant 2 \end{cases}$
D) $a_{n}=\begin{cases} 6,n=1 \\\\ 2n+2,n\geqslant 2 \end{cases}$

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