
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
A sequence $\{a_n\}$ is defined such that the "mean of the reciprocals" of its first $n$ terms is $\frac{1}{2n-1}$. Find the general formula for the $n^{\text{th}}$ term of the sequence.

Note: The "mean of the reciprocals" of $n$ positive numbers $p_1, p_2, \ldots, p_n$ is defined as $\frac{n}{p_1 + p_2 + \cdots + p_n}$.

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