
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 an ellipse with its foci on the $x$-axis, a major axis length of $4$, and a focal distance of $2$, find the standard equation of the ellipse;

(2) Given a hyperbola with asymptote equations $y=\pm \frac{3}{4}x$ and directrix equations $x=\pm \frac{16}{5}$, find the standard equation of the hyperbola.

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