
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 a parabola $C: y^2 = 2px$ ($p > 0$), a line passing through the focus $F$ of the parabola intersects the parabola at two points $A$ and $B$. If $|AF| = 8|OF|$ (where $O$ is the origin), find the ratio $\frac {|AF|}{|BF|}$.

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