
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
Let point $P(x,y)$ be a moving point on the circle: $x^{2}+(y-3)^{2}=1$, and let $A(2,0)$ and $B(-2,0)$ be fixed points. The maximum value of $\overrightarrow{PA} \cdot \overrightarrow{PB}$ is ______.

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