
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 tourists in a certain scenic area is increasing month by month. In February, the number of tourists was 16,000, and in April, the number of tourists was 25,000.
- $(1)$ Find the monthly average growth rate of the number of tourists in this scenic area for these two months.
- $(2)$ It is expected that the number of tourists in this scenic area will continue to increase in May, but the growth rate will not exceed the monthly average growth rate of the previous two months. It is known that from May 1st to May 21st, the scenic area has received 21,250 tourists. What is the maximum average number of tourists received per day in the next 10 days in May?

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