
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
On a blackboard, the positive integers $1, 2, \cdots, n$ (where $n \geq 3$) are written. Each time, two of these numbers $p$ and $q$ are replaced with $p+q$ and $|p-q|$. After several transformations, all the numbers become $k$. What possible values can $k$ take?

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