
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 the sequence $\left\{ a_n \right\}$ with the sum of its first $n$ terms $S_n = \frac{1}{3}a_n + \frac{2}{3}$, find the general formula for $\left\{ a_n \right\}$, which is $a_n = \_\_\_\_\_\_\_\_\_\_\_\_$

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