
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
In 2020, which is the year to achieve the goal of building a moderately prosperous society in all respects and to conclude the fight against poverty, our city has always placed industrial poverty alleviation in a prominent position and established two poverty alleviation planting bases, A and B. In order to support the poverty alleviation industries in our city, the poverty alleviation office contacted two fertilizer factories, C and D, to donate a total of 100 tons of fertilizer to our city, distributing these 100 tons of fertilizer evenly to the A and B planting bases. It is known that the amount of fertilizer donated by factory C is 20 tons less than twice the amount donated by factory D. The transportation costs of transporting the fertilizer from factories C and D to locations A and B are as shown in the table below:

|            | Factory C | Factory D |
|------------|-----------|-----------|
| To A (元/ton) | 22        | 20        |
| To B (元/ton) | 20        | 22        |

(1) Find the quantities of fertilizer donated by factories C and D, respectively;  
(2) Let x tons of fertilizer be transported from factory C to location A. Let y represent the total transportation cost of transporting the fertilizer from factories C and D to locations A and B. Find the functional relationship between y and x, and determine the minimum total transportation cost;  
(3) Due to the opening of a new road from factory D to location B, the transportation cost from factory D to location B is reduced by a (0 < a < 6) yuan per ton. How should the transportation be adjusted to minimize the total transportation cost?

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