
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 \\(A\\) be any point on the circle \\({x}^{2}+{y}^{2}=4 \\), and let line \\(l \\) be the line passing through point \\(A \\) and perpendicular to the \\(x \\)-axis. Let \\(D \\) be the intersection of line \\(l \\) with the \\(x \\)-axis, and let point \\(M \\) be on line \\(l \\), satisfying \\( \overrightarrow{DM}= \dfrac{ \sqrt{3}}{2} \overrightarrow{DA} .\\) As point \\(A\\) moves on the circle, let the trajectory of point \\(M \\) be curve \\(C \\). Find the equation of curve \\(C \\).

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