
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
Find the number of ordered pairs \((A, B)\) such that the following conditions hold:
- \(A\) and \(B\) are disjoint subsets of \(\{1,2, \ldots, 50\}\).
- \(|A|=|B|=25\)
- The median of \(B\) is 1 more than the median of \(A\).

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