
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 school tic-tac-toe tournament, 16 students participated, each playing exactly one game with every other participant. Players received 5 points for a win, 2 points for a draw, and 0 points for a loss. After the tournament, it was found that the total number of points scored by all participants was 550 points. What is the maximum number of participants who could have played without a single draw in the tournament?

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