
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
A tournament consists of matches between exactly three players, with each match awarding 2 points, 1 point, and 0 points to the players. Players who obtain no score are eliminated, and the remaining players are grouped into sets of three for subsequent matches. Some rounds may involve one or two players having a bye. If there are 999 players in the tournament, how many matches will have been played by the time a champion, the one who earned two points in the last match, is declared?

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