
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
With the arrival of the peak tourist season, the number of visitors to Beihu Wetland Park is increasing month by month. In March, the number of visitors was 80,000, and in May, the number of visitors was 125,000.
$(1)$ Find the monthly average growth rate of visitors to Beihu Wetland Park in these two months;
$(2)$ It is expected that the number of visitors to Beihu Wetland Park will continue to increase in June, but the growth rate will not exceed the monthly average growth rate of the previous two months. It is known that from June 1st to June 10th, Beihu Wetland Park has received 66,250 visitors. What is the maximum average number of visitors per day in the 20 days after June?

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