
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 Hyperbolic Man both decide to test their new cars on different tracks. Rational Man drives on a circular track parameterized by:
\begin{align*}
x &= \cos t, \\
y &= \sin t,
\end{align*}
Hyperbolic Man drives on a path parameterized by:
\begin{align*}
x &= -1 + 3 \cos \frac{t}{2}, \\
y &= 5 \sin \frac{t}{2}.
\end{align*}
Determine the smallest possible distance $AB$ between a point $A$ on Rational Man's track and a point $B$ on Hyperbolic Man's track.

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