
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
Medians \( AF \) and \( BE \) of triangle \( ABC \) intersect at point \( G \), and \( m\angle FGB = 60^\circ \). Given that \( AF = 10 \) and \( BE = 15 \), find the area of triangle \( ABC \).
A) \( \frac{50\sqrt{3}}{3} \)
B) \( \frac{75\sqrt{3}}{3} \)
C) \( \frac{100\sqrt{3}}{3} \)
D) \( \frac{125\sqrt{3}}{3} \)

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