
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 computer company located in Jinan has branches in both the city area and in Weishan Lake. The branch in the city has 6 computers, and the branch in Weishan Lake has 12 computers of the same model. A unit from Zibo wants to purchase 10 computers of this model, and a unit from Jinan wants to buy 8 computers of the same model. It is known that the transportation cost per computer from the city to Zibo and Jinan is 40 yuan and 30 yuan, respectively. The transportation cost per computer from Weishan Lake to Zibo and Jinan is 80 yuan and 50 yuan, respectively.

(1) Suppose x computers are transported from Weishan Lake to Zibo, express the total transportation cost y as a function of x.
(2) If the total transportation cost must not exceed 1000 yuan, how many transportation options are available?
(3) Determine the transportation plan with the lowest total cost and state what that cost is.

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