
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 that the focus of the parabola $C:y^{2}=2px\left(p \gt 0\right)$ is $F$, the directrix of $C$ intersects the $x$-axis at point $G$. A line passing through point $F$ with a slope of $\frac{4}{3}$ intersects $C$ at points $A$ and $B$ (point $A$ is above the $x$-axis). Find $\frac{|GA|}{|GB|}$.

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