
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
Given a hyperbola $\frac{y^{2}}{a^{2}}−\frac{x^{2}}{b^{2}}=1(a > 0,b > 0)$ with eccentricity $\frac{2\sqrt{3}}{3}$. Its asymptotes intersect the directrix of a parabola $(D)$: $y^{2}=2px(p > 0)$ at points $A$ and $B$. $O$ is the origin, and the area of $\triangle ABO$ is $2\sqrt{3}$.

(I) Find the equations of the asymptotes of hyperbola $(C)$;
(II) Find the value of $p$.

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