
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
A hyperbola has its center at the origin, with one focus at point $F(0, \sqrt{3})$. The distance between this focus and the nearest vertex is $\sqrt{3} - 1$. Determine the equation of the hyperbola.

A) $y^{2} - \dfrac{x^{2}}{2} = 1$
B) $x^{2} - \dfrac{y^{2}}{2} = 1$
C) $x^{2} - \dfrac{y^{2}}{\sqrt{2}} = 1$
D) $y^{2} - \dfrac{x^{2}}{\sqrt{2}} = 1$

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