
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 drive around two racetracks from time $t = 0$ to $t = \infty.$ Rational Woman drives along the path parameterized by
\[
\begin{align*}
x &= \sin t, \\
y &= \cos t,
\end{align*}
\]
and Irrational Woman drives along the path parameterized by
\[
\begin{align*}
x &= 2 + 3 \cos \frac{t}{\sqrt{3}}, \\
y &= 3 \sin \frac{t}{\sqrt{3}}.
\end{align*}
\]
If $C$ is a point on Rational Woman's racetrack, and $D$ is a point on Irrational Woman's racetrack, then find the smallest possible distance $CD.$

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