
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 an ellipse D: $\frac{x^2}{50} + \frac{y^2}{25} = 1$ and a circle M: $x^2 + (y-5)^2 = 9$, a hyperbola G shares the same foci with ellipse D, and its asymptotes are tangent to circle M. Determine the equation of hyperbola G.

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