
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
The focus of the parabola is on the $x$-axis, and the distance to the directrix is $10$.

(1) Find the standard equation of the parabola,

(2) Find the standard equation of the hyperbola and its asymptotes' equations, with the parabola's focus as one of its foci and the conjugate axis length equal to $8$.

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