
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 fruit merchant purchased 200 kilograms each of large and small cherries for $8000$ yuan each (assuming all were sold). The cost per kilogram of large cherries is $20$ yuan more than the cost per kilogram of small cherries.  
$(1)$ Find the cost per kilogram of large and small cherries.  
$(2)$ It is known that the selling price of large cherries is $40$ yuan per kilogram, and the selling price of small cherries is $16$ yuan per kilogram.  
① How much money did the fruit merchant earn after selling all the cherries?  
② The fruit merchant used $8000$ yuan again to purchase 200 kilograms each of large and small cherries for the second time. The cost per kilogram of large and small cherries remained the same, but during transportation, 20% of the small cherries were lost. If the selling price of small cherries remains the same, and the fruit merchant wants to earn no less than 90% of the money earned in the first time, what should be the minimum selling price per kilogram of large cherries?

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