
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 a hyperbola with the equation $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ $(a > 0, b > 0)$ and an eccentricity of $\sqrt{3}$, the line $x = -\frac{a^2}{c}$ ($c$ is the semi-latus rectum of the hyperbola) coincides with the latus rectum of the parabola $y^2 = 4x$. Determine the equation of this hyperbola.

A) $\frac{x^2}{3} - \frac{y^2}{6} = 1$
B) $\frac{x^2}{24} - \frac{y^2}{12} = 1$
C) $\frac{x^2}{6} - \frac{y^2}{3} = 1$
D) $\frac{x^2}{12} - \frac{y^2}{24} = 1$

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