
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 2023 Asian Games was successfully held in Hangzhou, and the mascot "Jiangnan Yi" became very popular. According to statistics, the sales volume of the "Jiangnan Yi" mascot on a certain e-commerce platform was 50,000 units in August and 72,000 units in October.
  
$(1)$ If the monthly average growth rate from August to October on the platform is the same, what is the monthly average growth rate?
  
$(2)$ Market research found that the cost price of the "Jiangnan Yi" mascot in a store is $40 per unit. If the selling price is $80 per unit, and 20 units can be sold per day, with an additional 2 units sold for every $0.5 decrease in price, the store decided to reduce the price for promotion and minimize inventory. If the store wants to make a daily profit of $1400 from selling this mascot, how much should the selling price be reduced by?

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