
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
Twelve participants are taking part in a chess tournament. After the tournament, each participant makes 12 lists as follows: 
- In the 1st list, each participant writes down only their own name.
- In the 2nd list, each participant writes down their own name and the names of all the opponents they defeated.
- In the 3rd list, each participant writes down all the names from their 2nd list as well as the names of all the opponents defeated by anyone in the 2nd list.
- This process continues until the 12th list, where each participant writes down all the names from their 11th list and the names of all the opponents defeated by anyone in the 11th list.

It is known that for each participant, their 12th list contains names that did not appear in their 11th list. How many draws were there in the tournament?

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