
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
Influenza, commonly known as the flu, is an acute respiratory infectious disease caused by the influenza virus. A city experienced an outbreak of the flu last November. According to statistics, on November 1st, there were 20 new cases of influenza virus infection in the city. After that, the number of new infections increased by an average of 50 people per day. Thanks to the measures taken by the city's medical department, the spread of the virus was controlled, and from a certain day onwards, the number of new infections decreased by an average of 30 people per day. By November 30th, a total of 8,670 people in the city were infected with the virus over these 30 days. On which day of November did the city have the highest number of new infections? And what was the number of new infections on that day?

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