
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 that $P$ is any point on the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{15}=1$, and $EF$ is any diameter of the circle $\odot N:(x-1)^{2}+y^{2}=4$, find the range of values for $\overrightarrow{P E} \cdot \overrightarrow{P F}$.

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