
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 construction site requires 120 tons of building materials every day. It is known that Material Site A can supply up to 80 tons per day, and Material Site B can supply up to 90 tons per day. If 50 tons of building materials are transported from Material Site A and 70 tons from Material Site B to the site, the total transportation cost is 26,000 yuan. If 75 tons of building materials are transported from Material Site A and 45 tons from Material Site B to the site, the total transportation cost is 27,000 yuan.  
(1) What is the transportation cost per ton of building materials from Material Sites A and B to the site?  
(2) Let the amount of materials transported from Material Site A be $a$ tons, and the total transportation cost be $W$ yuan. Write the function relationship between $W$ and $a$ (specify the range of the independent variable), and use knowledge of functions to explain how to arrange the transportation plan to minimize the daily total transportation cost. What is the lowest daily total transportation cost?

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