
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
A line passing through the focus \(F\) of the parabola \(y^2 = 4x\) intersects the parabola at points \(A\) and \(B\), with \(O\) being the origin. If \(\left|AF\right| = 3\), calculate the area of \(\triangle AOB\).

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