
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 that $F$ is the focus of the parabola $y^{2}=2px\left(p \gt 0\right)$, $O$ is the origin, and the line passing through the point $\left(4,0\right)$ intersects the parabola at points $A$ and $B$, such that $OA\bot OB$.  
$(1)$ Find the value of $p$;  
$(2)$ If $\angle AFB=120^{\circ}$, find the equation of the line $AB$.

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