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

A) $a_{n}=n(n+1)$

B) $a_{n}= \frac{n(n-1)}{2}$

C) $a_{n}= \frac{n(n+1)}{2}$

D) $a_{n}=n(n+1)+1$

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