
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
In a football tournament, 20 teams participated. Each team played one match against every other team. A team gets 3 points for a win, 1 point for a draw, and 0 points for a loss. After the tournament ended, Vasya calculated the total points scored by all the teams. The total was 500 points. How many matches ended in a draw?

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