
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 positive real numbers \(0 < a < b\), let \(x_1, x_2, x_3, x_4 \in [a, b]\). Find the minimum and maximum values of \(\frac{\frac{x_1^2}{x_2} + \frac{x_2^2}{x_3} + \frac{x_3^2}{x_4} + \frac{x_4^2}{x_1}}{x_1 + x_2 + x_3 + x_4}\).

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