
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
A parabola ($y^{2}=2px$) shares the same right focus as a hyperbola (${x^{2} \over 3}-y^{2}=1$).
(I) Find the equation of the parabola;
(II) Find the area of the triangle formed by the latus rectum of the parabola and the asymptotes of the hyperbola.

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