
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 $A(x_{0}, y_{0})(y_{0} > 0)$ is a point on the parabola $E: y^{2} = 2px (p > 0)$. When $x_{0} = 9$, $y_{0} = 6$. Find:<br/>
$(1)$ The standard equation of $E$;<br/>
$(2)$ Let $F$ be the focus of $E$, and the line $AF$ intersects $E$ at another point $B$, where $|AF| = 5$. Find the value of $\frac{|AF|}{|BF|}$.

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