
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
During the first eleven days, 700 people responded to a survey question. Each respondent chose exactly one of the three offered options. The ratio of the frequencies of each response was \(4: 7: 14\). On the twelfth day, more people participated in the survey, which changed the ratio of the response frequencies to \(6: 9: 16\). What is the minimum number of people who must have responded to the survey on the twelfth day?

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