
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 with the equation $\frac{x^2}{4} - \frac{y^2}{5} =1$, a parabola is formed with the hyperbola's center as its vertex and the hyperbola's right focus as its own focus. Determine the equation of the parabola.

A) $y^{2}=12x$
B) $y^{2}=-12x$
C) $y^{2}=6x$
D) $y^{2}=-6x$

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