
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
Let  $n \geq 3$  be an integer. Consider the set  $A=\{1,2,3,\ldots,n\}$ , in each move, we replace the numbers  $i, j$  by the numbers  $i+j$  and  $|i-j|$ . After doing such moves all of the numbers are equal to  $k$ . Find all possible values for  $k$ .

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