
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-robin hockey tournament, there were 2016 teams participating. According to the tournament regulations, 3 points are awarded for a win, 0 points for a loss, and in the case of a draw, extra time is played. The winner of the extra time receives 2 points, and the loser receives 1 point. After the tournament, Ostap Bender was informed of the number of points earned by each team, from which he concluded that at least $N$ matches ended with extra time. Find the maximum possible value of $N$.

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