
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
A group of young people went to dance at a disco, where each dance costs 1 yuan, and each boy dances exactly once with each girl. After this, they go to another place to dance, paying the same amount of money as before using alternative currency. Each person's entrance fee is 1 unit of alternative currency, and each dance costs 1 unit of alternative currency, with each person dancing twice with every other person (regardless of gender). They end up with 1 unit of alternative currency left. How many units of alternative currency can 1 yuan be exchanged for?

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