
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
Define $\frac{n}{P_1 + P_2 + \cdots + P_n}$ as the "average reciprocal" of $n$ positive numbers $p_1, p_2, \ldots, p_n$. If the "average reciprocal" of the first $n$ terms of the sequence $\{a_n\}$ is $\frac{1}{3n-1}$, then the general term formula of the sequence $\{a_n\}$ is $a_n = $ ______.

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