
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
The 2022 Winter Olympics will be jointly held in Beijing and Zhangjiakou. The mascot for the Winter Olympics is "Bing Duan Duan."  
$(1)$ According to market research, a factory produced a total of 500 "Bing Duan Duan" in February this year. In order to increase production, the factory has the same average monthly production growth rate. In April, the factory produced 720 "Bing Duan Duan." What is the average monthly production growth rate of the factory?  
$(2)$ It is known that a certain store can sell an average of 20 "Bing Duan Duan" per day, with a profit of 40 yuan each. If the price is reduced by 1 yuan, the store can sell 5 more items without reducing the price by more than 10 yuan. If the store needs to make a profit of 1440 yuan per day, how much should the price of each "Bing Duan Duan" be reduced by?

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