
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]


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The table below shows the quality and profit situation of three types of vegetables, A, B, and C, for shipping. A certain trucking company plans to ship types A, B, and C vegetables to be sold in other places (each truck is fully loaded according to regulations, and each truck can only carry one type of vegetable).

|                                | A   |     | B   |     | C    |
|--------------------------------|-----|-----|-----|-----|------|
| Tons of vegetables per truck   | 2   |     | 1   |     | 2.5  |
| Profit per ton (hundreds yuan) | 5   |     | 7   |     | 4    |

$(1)$ If 14 trucks are used to ship types B and C vegetables totaling 17 tons to location A for sale, how many trucks are used to ship types B and C vegetables respectively?

$(2)$ If 30 trucks are planned to ship types A, B, and C vegetables totaling 48 tons to location B for sale, with the requirement that the number of trucks carrying type A vegetables is no less than 1 and no more than 10, how should the shipping be arranged to maximize profit? Also, calculate the maximum profit.

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