
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 the parabola $C: x^{2}=2py (p > 0)$, with a focus at point $F$, and a point $M$ on the line $x-y-2=0$, let $MA$ and $MB$ be the two tangents of $C$ drawn through $M$ ($A$ and $B$ are the points of tangency). If the minimum value of $|AF| \cdot |BF|$ is $8$, find the value of $p$.

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