
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
Among 20 schoolchildren, a tennis tournament took place. Each participant played one match every day; by the end of 19 days, everyone had played exactly once with every other participant. There was only one tennis court in the school, so the matches were held one after another. Immediately after their first win in the tournament, a participant would receive a branded T-shirt. There are no draws in tennis. Petya was the eleventh participant to receive a T-shirt, and Vasya was the fifteenth. Petya received his T-shirt on the eleventh day of the tournament. On which day did Vasya receive his T-shirt?

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