
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
It's given that $F_1$ and $F_2$ are the left and right foci of the ellipse $C: \frac{x^2}{9} + \frac{y^2}{8} = 1$, and point $E$ is a moving point on the ellipse $C$. Calculate the maximum and minimum values of the dot product $\vec{EF}_1 \cdot \vec{EF}_2$.

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