
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 $x^{2}=4y$ with the focus $F$ and the directrix $l$, let $P$ be a point on the parabola. Draw a line $PA$ perpendicular to $l$ at point $A$. When $\angle AFO = 30^{\circ}$ ($O$ is the origin), find $|PF| =$ _____ .

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