
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
A survey of participants was conducted at the Olympiad.  $50\%$  of the participants liked the first round,  $60\%$  of the participants liked the second round,  $70\%$  of the participants liked the opening of the Olympiad. It is known that each participant liked either one option or all three. Determine the percentage of participants who rated all three events positively.

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