
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 \(\theta_{1}, \theta_{2}, \theta_{3}, \theta_{4} \in \mathbf{R}^{+}\) and \(\theta_{1}+\theta_{2}+\theta_{3}+\theta_{4}=\pi\), find the minimum value of \(\left(2 \sin ^{2} \theta_{1}+\frac{1}{\sin ^{2} \theta_{1}}\right)\left(2 \sin ^{2} \theta_{2}+\frac{1}{\sin ^{2} \theta_{2}}\right)\left(2 \sin ^{2} \theta_{3}+\frac{1}{\sin ^{2} \theta_{3}}\right)\left(2 \sin ^{2} \theta_{4}+\frac{1}{\sin ^{2} \theta_{4}}\right)\).

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