
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 with its center at the origin, left focus at $F(-\sqrt{3},0)$, and right vertex at $D(2,0)$,

(1) Find the standard equation of the ellipse;

(2) If $P$ is a moving point on the ellipse, a line perpendicular to the major axis is drawn through point $P$, with the foot of the perpendicular denoted as $Q$. Find the locus of the midpoint $M$ of line segment $PQ$.

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