
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
(14 points) A factory has two branches, one in location A and the other in location B, producing 12 and 6 machines respectively. Now, 10 machines are to be sold to area A and 8 to area B. It is known that the cost of transporting one machine from location A to area A and B is 400 yuan and 800 yuan respectively, and from location B to area A and B is 300 yuan and 500 yuan respectively.  
(1) Assume x machines are transported from location B to area A, find the function relationship of the total cost y with respect to x and determine its domain;  
(2) If the total cost does not exceed 9000 yuan, how many transportation methods are there?  
(3) Find the transportation plan with the lowest total cost and the lowest cost.

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