
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 a positive integer \(n \geq 3\), and real numbers \(x_1, x_2, \cdots, x_n\), not all zero, such that \(\sum_{k=1}^{n} x_k = 0\). Let \(A = \left(\sum_{k=1}^{n} x_k^3\right)^2\) and \(B = \left(\sum_{k=1}^{n} x_k^2\right)^3\). Find the maximum value of \(\frac{A}{B}\).

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