
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 sequence \(\{a_{n}\}\) such that \(a_{1}=\frac{1}{2}\) and \(a_{1} + a_{2} + \cdots + a_{n} = n^{2} a_{n}\) for \(n \geq 1\), find a general formula for \(a_{n}\). (1975 Canadian Olympiad problem)

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