
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 math competition consists of three problems, each of which receives an integer score from 0 to 7. For any two competitors, it is known that there is at most one problem in which they received the same score. Find the maximum number of competitors in this competition.

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