
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
Due to the extreme weather caused by the "El Niño phenomenon," a regional heatwave occurred in a certain area in July and August of 2022, reaching a special severe level, making it the strongest heatwave since 1961. To alleviate the impact of extreme weather on the area, a company donated a total of 120 tons of drinking water and vegetables to a town in the region, with the drinking water being 12 tons less than the vegetables.  
$(1)$ Find out how many tons of drinking water and vegetables were donated.  
$(2)$ It is planned to rent a total of 10 trucks of types A and B to transport all the drinking water and vegetables to the town. Each type A truck can carry up to 5 tons of drinking water and 8 tons of vegetables, while each type B truck can carry up to 6 tons of both drinking water and vegetables. How many arrangements are there for the company to use type A and type B trucks?  
$(3)$ Under the conditions of $(2)$, if the transportation cost is 400 yuan per type A truck and 360 yuan per type B truck, how should the company arrange the trucks to minimize the transportation cost? What is the minimum transportation cost?

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