
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 100 white stones arranged in a circle. An integer $k$ between 1 and 50 is given. In one move, it is allowed to choose any $k$ consecutive stones, the first and last of which are white, and paint the first and last stones black. For which values of $k$ is it possible to paint all 100 stones black in several such moves?

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