
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 that the center of a hyperbola is at the origin of the coordinate, its eccentricity $e = 2$, and one of its vertices coincides with the focus of the parabola $y^2 = -8x$, find the equation of this hyperbola.

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