
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
In the Cartesian coordinate system, let the focus of the parabola $y^2 = 4x$ be $F$, and the directrix be $l$. Let $P$ be a point on the parabola, and $PA$ be perpendicular to $l$, with $A$ as the foot of the perpendicular. If the angle of inclination of the line $AF$ is $120^\circ$, then $|PF|=$_______.

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