
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
The jury of the olympiad decided to assign a natural number to each participant based on their results, such that from this number it is possible to uniquely determine the points obtained by the participant for each problem. Additionally, among any two participants, the larger number should be assigned to the one who scored a higher total sum of points. Help the jury solve this problem!

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