
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
If \( p \) and \( q \) are positive integers, \(\max (p, q)\) is the maximum of \( p \) and \( q \) and \(\min (p, q)\) is the minimum of \( p \) and \( q \). For example, \(\max (30,40)=40\) and \(\min (30,40)=30\). Also, \(\max (30,30)=30\) and \(\min (30,30)=30\).

Determine the number of ordered pairs \((x, y)\) that satisfy the equation

$$
\max (60, \min (x, y))=\min (\max (60, x), y)
$$

where \(x\) and \(y\) are positive integers with \(x \leq 100\) and \(y \leq 100\).

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