
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 $\frac{x^{2}}{m} - \frac{y^{2}}{m+6} = 1 (m > 0)$, its conjugate axis is twice the length of its transverse axis. Determine the standard form of the hyperbola's equation.

A) $\frac{x^{2}}{2} - \frac{y^{2}}{4} = 1$
B) $\frac{x^{2}}{4} - \frac{y^{2}}{8} = 1$
C) $x^{2} - \frac{y^{2}}{8} = 1$
D) $\frac{x^{2}}{2} - \frac{y^{2}}{8} = 1$

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