
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 certain fruit plantation plans to rent several trucks to transport $60$ tons of apples and oranges to be sold in another city. Each truck can only carry one type of fruit and must be fully loaded.<br/>|               | Apples | Oranges |
|---------------|--------|---------|
| Capacity (tons) | $4$    | $6$     |
| Profit per ton (yuan) | $1200$ | $1500$  |
$(1)$ Let $x$ represent the number of trucks carrying apples and $y$ represent the number of trucks carrying oranges. Express $y$ in terms of $x$;<br/>$(2)$ Write the function relationship between the total profit $W$ (yuan) and the number of trucks $x$;<br/>$(3)$ If the number of trucks carrying apples must not be less than the number of trucks carrying oranges, how should they be arranged to maximize profit, and calculate the maximum profit.

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