
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
Rational Woman and Irrational Woman both buy new scooters, and they decide to ride around two racetracks from time $t = 0$ to $t = \infty.$ Rational Woman rides along the path parameterized by
\[
x = 2 \cos t, \quad y = 2 \sin t,
\]
and Irrational Woman rides along the path parameterized by
\[
x = -1 + 3 \cos \frac{t}{\sqrt{3}}, \quad y = 3 \sin \frac{t}{\sqrt{3}}.
\]
If $C$ is a point on Rational Woman's racetrack, and $D$ is a point on Irrational Woman's racetrack, find the smallest possible distance $CD.$

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