
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 real numbers \( a_{1}, a_{2}, \cdots, a_{2016} \) satisfying \( 9 a_{i} > 11 a_{i+1}^{2} \) for \( i = 1, 2, \cdots, 2015 \). 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}
user