
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
A point P is taken on the circle x²+y²=4. A vertical line segment PD is drawn from point P to the x-axis, with D being the foot of the perpendicular. As point P moves along the circle, what is the trajectory of the midpoint M of line segment PD? Also, find the focus and eccentricity of this trajectory.

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