
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 that the center of the ellipse E is at the coordinate origin O, its foci coincide with the foci of the hyperbola C: $x^2 - \frac{y^2}{2}=1$, and the two endpoints of the minor axis of the ellipse E and one of its foci form an equilateral triangle.
(1) Find the equation of the ellipse E;
(2) A line l is drawn through the right vertex A of the hyperbola C, intersecting the ellipse E at two distinct points P and Q. Let M be the point (m, 0). Find the value of m when $\overrightarrow {MP} \cdot \overrightarrow {MQ}$ is constant.

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