
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 a sequence of positive terms $\{a_n\}$, it holds that

$$
\frac{n}{a_{1} + 2a_{2} + 3a_{3} + \cdots + na_{n}} = \frac{2}{n + 2} \quad (n\in\mathbb{N^*}),
$$

find the general term $a_n$ of the sequence $\{a_n\}$.

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