
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
A certain breeding farm, in response to the poverty alleviation policy of the central government, has adopted the "farm + farmers" breeding model starting this year, while strengthening the scientific management of laying hens. The egg production rate of the laying hens continues to increase. The egg production in March and May is 25,000 kg and 36,000 kg, respectively. It is assumed that the monthly growth rate of egg production of the breeding farm's laying hens is the same.<br/>$(1)$ Find the monthly average growth rate of egg production of the breeding farm.<br/>$(2)$ Assuming that the eggs produced in a month are all sold out at each sales point, and the average monthly sales volume per sales point is at most 0.32 million kg. If the breeding farm needs to complete the egg sales task in June, how many additional sales points should be added to the existing sales points in May?

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