
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 $ABC$, medians $AF$ and $BE$ intersect at angle $\theta = 60^\circ$, where $AF = 10$ and $BE = 15$. Calculate the area of triangle $ABC$.
A) $150\sqrt{3}$
B) $200\sqrt{3}$
C) $250\sqrt{3}$
D) $300\sqrt{3}$

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