
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 races on a circular track defined by:
\[ x = \cos t, \, y = \sin t, \]
and Irrational Man races on another circular track defined by:
\[ x = -1 + 3 \cos \left(\frac{t}{2}\right), \, y = 3 \sin \left(\frac{t}{2}\right). \]
Find the shortest distance between any point \( A \) on Rational Man's track and any point \( B \) on Irrational Man's track.

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