
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 single-round hockey tournament, 2016 teams participated. According to the tournament rules, a victory earns 3 points, a loss earns 0 points, and in case of a tie, extra time is played. The winner of the extra time receives 2 points, and the loser receives 1 point. At the end of the tournament, Ostap Bender was told the number of points each team earned, based on which he concluded that at least \( N \) matches ended in extra time. Find the maximum possible value of \( N \).

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