
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
Let $F_1$ and $F_2$ be the left and right foci of the ellipse $C$: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}} = 1 \quad (a > b > 0)$$ respectively.  
(Ⅰ) If the sum of the distances from a point $A(1, \frac {3}{2})$ on the ellipse to points $F_1$ and $F_2$ equals 4, find the equation of ellipse $C$;  
(Ⅱ) Let point $P$ be a moving point on the ellipse $C$ obtained in (Ⅰ), find the equation of the trajectory of the midpoint $M$ of the line segment $F_1P$.

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