
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 parabola $y^2 = 4x$ has a focus at point $F$. A line passing through $F$ intersects the upper part of the parabola at point $A$ and intersects the directrix $l$ at point $B$, where $AK \perp l$ at $K$. If $|AF| = |BF|$, calculate the area of $\Delta AKF$.

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