
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
There are 47 students in a class, with the classroom arranged in 6 rows and 8 columns. Each seat can be denoted as \((i, j)\) where \(i\) is the row number and \(j\) is the column number. At the beginning of the new semester, seats will be rearranged such that a student originally seated at \((i, j)\) is moved to \((m, n)\). The movement of the student is described by \([a, b] = [i - m, j - n]\), and the sum \(a + b\) is referred to as the student's position number. The total sum of all students' position numbers is denoted as \(S\). Determine the difference between the maximum and minimum possible values of \(S\).

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