
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 non-zero plane vectors $\overrightarrow{m}, \overrightarrow{n}$, and $\theta=(\overrightarrow{m}, \overrightarrow{n})$. Define $\overrightarrow{m} \otimes \overrightarrow{n} = |\overrightarrow{m}| \times |\overrightarrow{n}| \sin \theta$. $F_{1}$ and $F_{2}$ are the left and right foci of the ellipse $C$: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$, and points $M$ and $N$ are its top and right vertices, respectively, with $\overrightarrow{OM} \otimes \overrightarrow{ON} = 6\sqrt{2}$, and the eccentricity $e = \frac{1}{3}$.
(Ⅰ) Find the equation of the ellipse $C$;
(Ⅱ) A line passing through point $F_{2}$ intersects the ellipse $C$ at points $A$ and $B$. Find the range of values for $\overrightarrow{OA} \otimes \overrightarrow{OB}$.

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