
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 $C$: $y^{2}=8x$ with focus $F$ and directrix $l$. $P$ is a point on $l$, and the line $PF$ intersects the parabola at points $M$ and $N$. Find the length $|MN|$ given $\overrightarrow{PF}=3\overrightarrow{MF}$.

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