
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 mathematical contest had  $3$  problems, each of which was given a score between  $0$  and  $7$  ( $0$  and  $7$  included). It is known that, for any two contestants, there exists at most one problem in which they have obtained the same score (for example, there are no two contestants whose ordered scores are  $7,1,2$  and  $7,1,5$ , but there might be two contestants whose ordered scores are  $7,1,2$  and  $7,2,1$ ). Find the maximum number of contestants.

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