
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 $C: x^{2}=4y$ with focus $F$, and the line $l: x=5$, points $A$ and $B$ are moving points on the parabola $C$ and line $l$, respectively. If point $B$ is in a certain position where there exists only one point $A$ such that $|AF|=|AB|$, then the values of $|AB|$ that satisfy the condition are ______.

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