
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 ${a_{n}}$, where $a_{1}=1$ and the sum of the first $n$ terms $S_{n}=\frac{n+2}{3}{a_{n}}$.

(1) Find $a_{2}$ and $a_{3}$;

(2) Find the general formula for the sequence ${a_{n}}$.

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