
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
An essay in Latin is graded with a score from 0 to 20. Michel's score exceeds the average score, and Claude's score is below the average. What score did each of them receive, given that subtracting one-third of the lower score from each of these two scores results in one remainder that is three times the other remainder?

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