
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 \(f(n) = \frac{x_1 + x_2 + \cdots + x_n}{n}\), where \(n\) is a positive integer and \(x_k = k^2\) for \(k = 1, 2, \ldots, n\), find the expression for \(f(n)\).

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