
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 equation of an ellipse is $\frac{x^2}{49} + \frac{y^2}{24} = 1$,
(1) Find the coordinates of the foci and vertices of the ellipse;
(2) Find the equation of the hyperbola with the foci of the ellipse as its vertices and the vertices of the ellipse as its foci.

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