
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
Meghal is playing a game with 2016 rounds \(1, 2, \cdots, 2016\). In round \(n\), two rectangular double-sided mirrors are arranged such that they share a common edge and the angle between the faces is \(\frac{2 \pi}{n+2}\). Meghal shoots a laser at these mirrors and her score for the round is the number of points on the two mirrors at which the laser beam touches a mirror. What is the maximum possible score Meghal could have after she finishes the game?

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