
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
Genius Man and Adventurous Man both decide to race their cars from time $t = 0$ to $t = \infty$. Genius Man drives along a circular track parameterized by:
\[
x = 2\cos t, \quad y = 2\sin t,
\]
and Adventurous Man drives along an elliptical path parameterized by:
\[
x = 3 + 3\cos \frac{t}{2}, \quad y = 3\sin \frac{t}{2}.
\]
If $C$ is a point on Genius Man's track, and $D$ is a point on Adventurous Man's track, determine the smallest possible distance $CD$.

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