
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

Let the real numbers \(a_1, a_2, \cdots, a_{2016}\) satisfy
\[
9 a_i > 11 a_{i+1}^2 \quad (i = 1, 2, \cdots, 2015).
\]

Find the maximum value of 
\[
\left(a_1 - a_2^2\right)\left(a_2 - a_3^2\right) \cdots \left(a_{2015} - a_{2016}^2\right)\left(a_{2016} - a_1^2\right).
\]

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