
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
Out of 500 participants in a remote math olympiad, exactly 30 did not like the problem conditions, exactly 40 did not like the organization of the event, and exactly 50 did not like the method used to determine the winners. A participant is called "significantly dissatisfied" if they were dissatisfied with at least two out of the three aspects of the olympiad. What is the maximum number of "significantly dissatisfied" participants that could have been at this olympiad?

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