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

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