
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
(1) Given that a hyperbola and an ellipse share the same foci, with the ellipse defined by the equation $\frac{y^2}{49} + \frac{x^2}{24} = 1$, and the hyperbola has asymptotes $y = \pm \frac{4}{3}x$, find the equation of the hyperbola.
(2) Given that an ellipse passes through points $A(0, \frac{5}{3})$ and $B(1, 1)$, find the standard equation of the ellipse.

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