
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 a certain city, an influenza outbreak occurred in November last year. According to statistics, there were 20 new cases of influenza virus infection on November 1st. 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. Starting from a certain day, the number of new infections decreased by an average of 30 people per day. By November 30th, a total of 8670 people in the city were infected with the virus during these 30 days. What was the date in November when the number of new infections in the city reached its peak? And calculate the number of new infections on that day.

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