
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 one asymptote of the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 (a > 0, b > 0)$ is parallel to the line $y = x + 2$, and its focus coincides with the focus of the ellipse $\frac{x^{2}}{24} + \frac{y^{2}}{16} = 1$, find the equation of the hyperbola.

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