
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 Man and Irrational Man again choose to drive around two racetracks continuously from time $t = 0$ to $t = \infty$. Rational Man's racetrack is given by the circle parameterized as:
\begin{align*}
x &= \cos t, \\
y &= \sin t,
\end{align*}
Irrational Man's racetrack is now given by the new ellipse parameterized as:
\begin{align*}
x &= 3 + 2 \cos \frac{t}{\sqrt{3}}, \\
y &= 3 \sin \frac{t}{\sqrt{3}}.
\end{align*}
Find the smallest possible distance $AB$ where $A$ is a point on the circle and $B$ on the ellipse.

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