
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 that \( x_{1}, x_{2}, x_{3}, x_{4} \) are all positive numbers and \( x_{1} + x_{2} + x_{3} + x_{4} = \pi \), find the minimum value of the expression \(\left(2 \sin^2 x_{1}+\frac{1}{\sin^2 x_{1}}\right)\left(2 \sin^2 x_{2}+\frac{1}{\sin^2 x_{2}}\right)\left(2 \sin^2 x_{3}+\frac{1}{\sin^2 x_{3}}\right)\left(2 \sin^2 x_{4}+\frac{1}{\sin^2 x_{4}}\right)\).

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