
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
If the acute angles \( A, B, C \) satisfy \( \sin^2 A + \sin^2 B + \sin^2 C = 2 \), find the minimum value of \( \frac{1}{\sin^2 A \cos^4 B} + \frac{1}{\sin^2 B \cos^4 C} + \frac{1}{\sin^2 C \cos^4 A} \).

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