
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
Consider the ellipse $\frac{x^{2}}{72} + \frac{y^{2}}{36} = 1$ with left and right foci $F_1$ and $F_2$, respectively. If a point $M$ on the ellipse satisfies $\angle F_1MF_2 = 60^\circ$, find the area of $\triangle F_1MF_2$.

A) $12\sqrt{3}\quad\quad\quad\quad$
B) $24\sqrt{3}$
C) $12\sqrt{2}$
D) $24$

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