
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 factory has two branches, one in location A and the other in location B, producing 12 and 6 machines respectively. Now, they need to distribute 10 machines to area A and 8 machines to area B. It is known that the transportation cost for moving one machine from location A to area A and B is 400 and 800 yuan respectively, and from location B to area A and B is 300 and 500 yuan respectively.  
(Ⅰ) Assume x machines are transported from location B to area A, derive the function expression of the total cost y in terms of the number of machines x;  
(Ⅱ) If the total transportation cost does not exceed 9000 yuan, how many transportation plans are there?  
(Ⅲ) 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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