
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 $F_1$ and $F_2$ be the two foci of the ellipse $\frac{x^2}{4} + y^2 = 1$, and let point $P$ be a moving point on this ellipse. Find the range of values for $\overrightarrow{PF_1} \cdot \overrightarrow{PF_2}$.

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