
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
In the rectangular coordinate system $(xOy)$, a semicircle $C$ has the polar coordinate equation $\rho = 2\cos\theta$, where $\theta \in [0, \frac{\pi}{2}]$, with the origin as the pole and the positive $x$-axis as the polar axis.

(1) Find the parametric equations of $C$.

(2) Let $D$ be a point on $C$ such that the tangent line to $C$ at $D$ is perpendicular to the line $l: y = \sqrt{3}x + 2$. Using the parametric equations obtained in part (1), determine the coordinates of $D$.

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