
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
12 chess players participated in a round-robin tournament. Afterwards, each player wrote 12 lists. The first list contains only himself, the $(k+1)$-th list contains the players from the $k$-th list and those who were defeated by any of the players in the $k$-th list. It turned out that the 12th list of each player is different from their 11th list. How many draws were there?

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