
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
Point $F$ is the focus of the parabola $x^{2}=8y$ and point $A$ is the left vertex of the hyperbola $\frac{{x}^{2}}{8}-\frac{{y}^{2}}{b}=1$. Given that the line $AF$ is parallel to one of the asymptotes of the hyperbola $C$, determine the value of the real number $b$.

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