
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 a parabola $y^{2}=2px(p > 0)$ with its focus $F$, a line through the focus $F$ intersects the parabola at points $A$ and $B$, and $\overrightarrow{AF}=3\overrightarrow{FB}$. The directrix $l$ of the parabola intersects the $x$-axis at point $C$, and $AA_{1}\perp l$ at point $A_{1}$. If the area of the quadrilateral $AA_{1}CF$ is $12\sqrt{3}$, find the equation of the directrix $l$.

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