
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
The sequence \(a_{1}, a_{2}, a_{3}, \cdots\) satisfies (1) \(a_{1}=\frac{1}{2}\), (2) \(a_{1}+a_{2}+\cdots+a_{n}=n^{2} a_{n} \text { for } n \geqslant 2\). Find \(a_{n}\).

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