
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
Let the parabola $C: y= \frac{1}{4}x^2$ have its focus at point $F$, and let a line $l$ pass through the focus $F$ and intersect the parabola $C$ at points $A$ and $B$, with $|AF| = 3$. Find the ratio $\frac{S_{\triangle AOF}}{S_{\triangle BOF}}$.

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