
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 $l$, let $P$ be a point on $l$, and $Q$ be a point where the line $PF$ intersects $C$. Let $O$ be the origin. If $\overrightarrow {FP} = 4 \overrightarrow {FQ}$, then find the value of $|QO|$.

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