
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
Given a rectangle \(ABCD\) with \(AB = b\) and \(AD = a\) where \(a \geq b\), three points \(X\), \(Y\), and \(Z\) are placed anywhere on or inside the rectangle. Find the maximum value of the minimum distance between any two of these points (expressed in terms of \(a\) and \(b\)).

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