
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
Let $F$ be the focus of the parabola $C$: $y^{2}=2px(p > 0)$, and the line $x-2y-3p=0$ intersects $C$ at points $A$ and $B$. Let $O$ be the origin. Given the area of $\triangle FAB$ is $5 \sqrt {10}$, find the value of $p$.

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