
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
Given the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{3} = 1$ with left and right foci $F_1$ and $F_2$, respectively. A circle with radius $a$ is centered at one of the foci, and it is tangent to both asymptotes of the hyperbola at points $A$ and $B$. Find the area of the quadrilateral $F_1AF_2B$.

A) 3
B) 4
C) 5
D) 6

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