
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 the positive sequence \(\left\{a_{n}\right\}\) with the first term being 1, and for any positive integer \(n\), the following relation holds:
\[ a_{n}\left(n a_{n}-a_{n+1}\right)=(n+1) a_{n+1}^{2} . \]

Find \(a_{n}\).

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