
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 parabola $y^{2}=4x$, and a line $l$ passes through the focus $F$ of the parabola and intersects the parabola at points $A$ and $B$ (point $A$ is in the first quadrant) and $\overrightarrow{BA}=4\overrightarrow{BF}$, calculate the area of $\Delta AOB$ (where $O$ is the origin).

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