
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 \(0 < a < b\), suppose \(x_{1}, x_{2}, x_{3}, x_{4} \in [a, b]\). 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