
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 the positive real numbers \(a_{1}, a_{2}, a_{3}, a_{4}\) satisfy the conditions \(a_{1} \geqslant a_{2} a_{3}^{2}, a_{2} \geqslant a_{3} a_{4}^{2}, a_{3} \geqslant a_{4} a_{1}^{2}, a_{4} \geqslant a_{1} a_{2}^{2}\), find the maximum value of \(a_{1} a_{2} a_{3} a_{4}\left(a_{1}-a_{2} a_{3}^{2}\right)\left(a_{2}-a_{3} a_{4}^{2}\right)\left(a_{3}-a_{4} a_{1}^{2}\right)\left(a_{4}-a_{1} a_{2}^{2}\right)\).

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