
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
In a certain village, the average income per capita was 20,000 yuan in the year 2018, and 24,200 yuan in the year 2020.  
$(1)$ Find the annual average growth rate of the per capita income in the village from 2018 to 2020.  
$(2)$ Assuming that the growth rate of per capita income in the village in 2021 is the same as the annual average growth rate of the previous two years, predict how much the per capita income in the village will be in 2021.

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