
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 ellipse \(\frac{x^{2}}{4} + y^{2} = 1\) and a point \(P\) on the circle \(x^{2} + y^{2} = 16\), where lines \(PA\) and \(PB\) are tangent to the ellipse at points \(A\) and \(B\) respectively, find the maximum and minimum values of \(\overrightarrow{P A} \cdot \overrightarrow{P B}\).

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