
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 its center at the origin and its foci on the $x$-axis, and the distance between the foci is $2$, the eccentricity is $e= \frac { \sqrt {2}}{2}$.  
(Ⅰ) Find the equation of the ellipse $E$;  
(Ⅱ) A line $l$ passes through the point $(1,0)$ and intersects $E$ at points $P$ and $Q$. Is there a fixed point $M$ on the $x$-axis such that $ \overrightarrow{MP}\cdot \overrightarrow{MQ}$ is a constant value? If it exists, find the coordinates of this fixed point $M$; if not, explain why.

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