
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]


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Given a sequence of positive terms $\{a\_n\}$, define $H\_n = \frac{n}{a\_1 + 2a\_2 + 3a\_3 + \ldots + na\_n}$ as the "sunshine" value of the sequence $\{a\_n\}$. If it is known that the "sunshine" value of a certain sequence is $H\_n = \frac{2}{n+2}$, find the general term formula for the sequence $\{a\_n\}$.

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