
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 $C: \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 (a, b > 0)$ with left and right foci $F_1$ and $F_2$, respectively. A line perpendicular to one of the asymptotes of hyperbola $C$ passes through $F_2$ and intersects it at point $H$. If the area of $\triangle HF_1F_2$ is $a^2$, determine the eccentricity of the hyperbola.

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

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