
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 parametric equation of a parabola as \\(\begin{cases}x=4{t}^{2} \\\\ y=4t\\end{cases} \\) (where $t$ is the parameter), the focus is $F$, the directrix is $l$, and a point $P$ on the parabola with $PE⊥l$ at $E$. If the angle of inclination of line $EF$ is $150{}^\\circ$, find $|PF|$.

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