
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
The minimum distance from a moving point $A$ on the parabola $y^{2}=2 p\left(x-\frac{p}{2}\right)(p>0)$ to the point $B(3,0)$ is denoted as $d(p)$. The sum of all real numbers $p$ that satisfy $d(p)=2$ is ______.

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