
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 the curve $C$: $y^{2}=4x$ with a focus at point $F$, a line $l$ passes through point $F$ and intersects curve $C$ at points $P$ and $Q$. If the relationship $\overrightarrow{FP}+2\overrightarrow{FQ}=\overrightarrow{0}$ holds, calculate the area of triangle $OPQ$.

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