
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 a curve $E$ where any point $P$ on it has a constant sum of distances to two fixed points $F_{1}(-\sqrt{3},0)$ and $F_{2}(\sqrt{3},0)$ equal to $4$.  
(Ⅰ) Find the equation of curve $E$;  
(Ⅱ) Let point $A(1,1)$, if $P$ is a moving point on curve $E$, find the equation of the trajectory of the midpoint $M$ of segment $PA$.

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