
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 sequence $\{a_n\}$ satisfies $\frac{1}{3}a_1+ \frac{1}{3^2}a_2+\ldots+ \frac{1}{3^n}a_n=3n+1$, where $n\in\mathbb{N}^*$, then $a_n=$ ______.

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