
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
100 couples are invited to a traditional Modolvan dance. The  $200$  people stand in a line, and then in a  $\textit{step}$ , (not necessarily adjacent) many swap positions. Find the least  $C$  such that whatever the initial order, they can arrive at an ordering where everyone is dancing next to their partner in at most  $C$  steps.

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