
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
There are 16 players participating in an advanced chess tournament, where each pair of players plays exactly one game. The winner of each game earns 1 point, the loser earns 0 points. If a game ends in a draw, each player earns 0.5 points. After all games are completed, players who have accumulated at least 10 points advance to the next stage. What is the maximum number of players who can advance?

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