
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 are racing on two separate tracks. Rational Man drives a path parameterized by:
\[
x = 2\cos t, \\
y = 2\sin t,
\]
and Irrational Man drives a path parameterized by:
\[
x = 2 + 3\cos \frac{t}{\sqrt{2}}, \\
y = 5\sin \frac{t}{\sqrt{2}}.
\]
Find the minimum possible distance between a point $A$ on Rational Man's track and a point $B$ on Irrational Man's track.

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