
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
Define the real sequence \(a_1, a_2, a_3, \ldots\) by \(a_1 = \frac{1}{2}\), and \(n^2 a_n = a_1 + a_2 + \ldots + a_n\). Evaluate \(a_n\).

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