
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 $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$, where $F\_1$ and $F\_2$ are the left and right foci of the ellipse, and $M$ is any point on the ellipse. If the range of values for $\overrightarrow{MF_{1}} \cdot \overrightarrow{MF_{2}}$ is $[-3, 3]$, find the equation of the ellipse.

A) $\frac{x^{2}}{9}+ \frac{y^{2}}{3}=1$
B) $\frac{x^{2}}{6}+ \frac{y^{2}}{3}=1$
C) $\frac{x^{2}}{12}+ \frac{y^{2}}{4}=1$
D) $\frac{x^{2}}{4}+ y^{2}=1$

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