
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 \( a_{1}, a_{2}, \ldots, a_{2016} \) satisfy \( 9a_{i} > 11a_{i+1}^2 \) for \( i = 1, 2, \ldots, 2015 \). Find the maximum value of \[ \left(a_{1}-a_{2}^{2}\right) \cdot \left(a_{2}-a_{3}^{2}\right) \cdots \cdot \left(a_{2015}-a_{2016}^{2}\right) \cdot \left(a_{2016}-a_{1}^{2}\right) \].

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