
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]


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The jury is preparing versions of an olympiad for 5th, 6th, 7th, 8th, 9th, and 10th grades. The jury members agreed that each version should contain seven problems, exactly four of which do not appear in any other version. What is the maximum number of problems that can be included in such an olympiad?

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