
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
$$
\begin{array}{l}
9 a_{i}>11 a_{i+1}^{2} \text{ for } i=1,2, \cdots, 2015.
\end{array}
$$
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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