
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 triangle \(ABC\), it is known that \(AB = 4\), \(AC = 6\), and \(\angle BAC = 60^\circ\). The extension of the angle bisector \(AA_1\) intersects the circumcircle of triangle \(ABC\) at point \(A_2\). Find the areas of triangles \(OA_2C\) and \(A_1A_2C\) where \(O\) is the center of the circumcircle of triangle \(ABC\).

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