
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
In an olympiad, 55 students participated, and all of them submitted their work. For each problem, one of the three assessments was given: "+" - the problem was solved, "-" - the problem was attempted, "0" - the problem was not attempted. After evaluating all the works, it was found that no two works had the same number of "+" and "-" simultaneously. What is the minimum number of problems that could have been proposed in the olympiad?

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