
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 a parabola $y^2=2px$ ($p>0$) whose focus lies on the line $2x-y-4=0$, find the value of $p$.
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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