
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 start driving their cars on separate racetracks at time $t = 0$ and continue indefinitely. Rational Woman follows the path parameterized by
\[
x = \sin t, \quad y = \cos t,
\]
while Irrational Woman drives along the path given by
\[
x = -2 + 3 \cos \left(\frac{t}{2}\right), \quad y = 2 + 3 \sin \left(\frac{t}{2}\right).
\]
Determine the minimum distance between a point $A$ on Rational Woman's track and a point $B$ on Irrational Woman's track.

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