
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  $m+n$  numbers:  $a_i,$   $i = 1,2, \ldots, m,$   $b_j$ ,  $j = 1,2, \ldots, n,$  determine the number of pairs  $(a_i,b_j)$  for which  $|i-j| \geq k,$  where  $k$  is a non-negative integer.

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