
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
On February 25, 2021, China solemnly declared to the world that China had achieved a comprehensive victory in the fight against poverty, creating another remarkable miracle in human history. During the process of poverty alleviation, a certain impoverished household had an average annual per capita net income of 3200 yuan in 2018. Through government support in developing animal husbandry, the household's average annual per capita net income increased to 5000 yuan by 2020, successfully lifting them out of poverty.
  
$(1)$ Calculate the annual average growth rate of the household's average annual per capita net income in 2019 and 2020.
  
$(2)$ If the annual average growth rate remains the same, can the household's average annual per capita net income reach 6200 yuan by the end of 2021?

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