
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
Our company organized 20 trucks to transport a total of 100 tons of fruits A, B, and C to be sold in other places. According to the plan, all 20 trucks need to be loaded, each truck can only carry the same kind of fruit, and must be fully loaded. Based on the information provided in the table, answer the following questions:

| Fruit | A   | B   | C   |
|-------|-----|-----|-----|
| Tons per truck | 6 | 5 | 4 |
| Profit per ton (in yuan) | 500 | 600 | 400 |

1. Let $x$ be the number of trucks arranged to transport fruit A, and $y$ be the number of trucks arranged to transport fruit B. Find the functional relationship between $y$ and $x$.
2. If the number of trucks transporting the three types of fruits is not less than 2 each, how should the transportation plan be arranged to maximize the profit from selling all three types of fruits? What is the maximum profit?

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