
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 a certain city, locations $A$ and $B$ need fertilizers for autumn planting, requiring 80 tons and 70 tons, respectively. Locations $C$ and $D$ in the city store 100 tons and 50 tons of fertilizers, respectively. All the fertilizers are to be transported to locations $A$ and $B$. The transportation costs (in yuan per ton) from locations $C$ and $D$ to locations $A$ and $B$ are shown in the table below:

| Departure | Destination | Cost (yuan/ton) |
|-----------|-------------|-----------------|
| $C$       | $A$         | $25$            |
| $D$       | $A$         | $30$            |
| $C$       | $B$         | $20$            |
| $D$       | $B$         | $35$            |

$(1)$ Let the amount of fertilizer transported from location $C$ to location $A$ be $x$ tons. Then, the amount of fertilizer transported from location $C$ to location $B$ is ______ tons, from location $D$ to location $A$ is ______ tons, and from location $D$ to location $B$ is ______ tons.

$(2)$ Express the total transportation cost $W$ (in yuan) as an algebraic expression involving $x$ tons, and calculate the total transportation cost when $x=40$ tons.

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