
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 $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ $(a > b > 0)$, one of its foci coincides with the focus F of the parabola $y^{2}=4\sqrt{3}x$, and the two endpoints of the minor axis of the ellipse form an equilateral triangle with F.

(Ⅰ) Find the equation of the ellipse;

(Ⅱ) If a line l passes through the point (1, 0) and intersects the ellipse at two distinct points P and Q, is there a fixed point E (m, 0) on the x-axis such that $\overrightarrow{PE} \cdot \overrightarrow{QE}$ is always a constant value? If such a point exists, determine the coordinates of E and the constant value; if not, explain why.

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