
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
Along the edge of a round table, there are $n$ bowls placed at equal distances. A person starts a game by choosing a bowl and placing one bean in it. Next, they place one bean in the adjacent bowl in the clockwise direction. Then, they continue moving in the clockwise direction, skipping one bowl and placing one bean in the next bowl. They keep skipping one more bowl than before and placing one bean in the next bowl each time. The game continues until there is at least one bean in each bowl. For which positive integers $n$ can this game be completed in a finite number of steps?

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