
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
Determine the equations of the curves based on the following conditions:
(I) Find the equation of the hyperbola that shares the same asymptotes as the hyperbola $\frac{x^2}{16} - \frac{y^2}{9} = 1$ and passes through point A $(2\sqrt{3}, -3)$.
(II) Find the equation of the ellipse with the same eccentricity as the ellipse $\frac{x^2}{4} + \frac{y^2}{3} = 1$ that passes through the point $(2, -\sqrt{3})$.

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