
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 Spring Festival holiday in 2022, Shunde Overseas Chinese Town received a total of 200,000 visitors, and it is expected to receive 288,000 visitors during the Spring Festival holiday in 2024.<br/>$(1)$ Find the average annual growth rate of visitors to Shunde Overseas Chinese Town during the Spring Festival holidays from 2022 to 2024;<br/>$(2)$ A milk tea shop in Overseas Chinese Town sells a type of milk tea with a cost price of 6 yuan per cup. Based on sales experience, during the peak tourist season, if the price per cup is set at 25 yuan, an average of 300 cups can be sold per day. If the price per cup is reduced by 1 yuan, an average of 30 more cups can be sold per day. During the Spring Festival period in 2024, the shop decides to conduct a price reduction promotion. What should be the selling price per cup so that customers can get the maximum discount and the shop can achieve an average daily profit of 6,300 yuan on this type of milk tea?

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