
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: call the expression $$\frac {n}{p_{1}+p_{2}+\cdots +p_{n}}$$ the "harmonic mean" of n positive numbers $p_1, p_2, \ldots, p_n$. If the "harmonic mean" of the first n terms of the sequence $\{a_n\}$ is $$\frac {1}{2n-1}$$, then the general term formula for the sequence $\{a_n\}$ is \_\_\_\_\_\_.

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