
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

In the diagram, \(ABCDEF\) is a regular hexagon with side length 4 and center \(O\). The line segment perpendicular to \(OA\) and passing through \(A\) meets \(OB\) extended at \(P\). What is the area of \(\triangle OAP\)?

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