
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 plan is to transport 1240 tons of goods A and 880 tons of goods B using a fleet of trucks to a certain location. The fleet consists of two different types of truck carriages, A and B, with a total of 40 carriages. The cost of using each type A carriage is 6000 yuan, and the cost of using each type B carriage is 8000 yuan.

(1) Write a function that represents the relationship between the total transportation cost (y, in ten thousand yuan) and the number of type A carriages used (x);

(2) If each type A carriage can carry a maximum of 35 tons of goods A and 15 tons of goods B, and each type B carriage can carry a maximum of 25 tons of goods A and 35 tons of goods B, find all possible arrangements of the number of type A and type B carriages to be used according to this requirement;

(3) Among these arrangements, which one has the minimum transportation cost, and what is the minimum cost?

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