
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  $n$  students standing in line positions  $1$  to  $n$ . While the teacher looks away, some students change their positions. When the teacher looks back, they are standing in line again. If a student who was initially in position  $i$  is now in position  $j$ , we say the student moved for  $|i-j|$  steps. Determine the maximal sum of steps of all students that they can achieve.

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