
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
If point $P$ is on the parabola $x^{2}=4y$, $F$ is the focus of the parabola, and $|PF|=5$, and a circle with $P$ as the center and $|PF|$ as the radius intersects the $x$-axis at points $A$ and $B$, calculate the dot product of $\overrightarrow{AP}$ and $\overrightarrow{AB}$.

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