
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 $\frac{x^2}{m^2} - \frac{y^2}{n^2} = 1$ (where $m > 0, n > 0$) with a focal length of $\sqrt{7}$ and an asymptote with the equation $y = \sqrt{6}x$, determine the equation of this hyperbola.

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