
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 an ellipse E with the equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a > b > 0$) and a focal distance of 4, find the chord passing through one of the foci and perpendicular to the x-axis that has a length of $2\sqrt{2}$.
(Ⅰ) Find the equation of ellipse E.
(Ⅱ) Let line l pass through the right focus of ellipse E and intersect the ellipse at points M and N. Assuming the left focus is F, determine the range of the dot product $\overrightarrow{FM} \cdot \overrightarrow{FN}$.

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