
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 classroom with seats arranged in 6 rows  $ \times$  8 columns, and the seat in the  $ i$ -th row and  $ j$ -th column is denoted by  $ (i,j).$  Now, an adjustment is made for students’ seats in the new school term. For a student with the original seat  $ (i,j),$  if his/her new seat is  $ (m,n),$  we say that the student is moved by  $ [a, b] \equal{} [i \minus{} m, j \minus{} n]$  and define the position value of the student as  $ a\plus{}b.$  Let  $ S$  denote the sum of the position values of all the students. Determine the difference between the greatest and smallest possible values of  $ S.$ 

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