
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 $AB=3$, $AC=4$, 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 $A_1A_2C$ ($O$ is the center of the circumcircle of triangle $ABC$).

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