
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) If the focus of a parabola is the left vertex of the ellipse $\frac {x^{2}}{64}+ \frac {y^{2}}{16}=1$, find the standard equation of this parabola;
(2) If a hyperbola shares its foci with the ellipse $\frac {x^{2}}{64}+ \frac {y^{2}}{16}=1$ and has asymptotes of $y=± \sqrt {3}x$, find the standard equation of this hyperbola.

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