
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 merchant purchased 20 boxes of a certain type of apples. Each box of apples is based on a standard weight of 25 kilograms. Any excess weight is recorded as a positive number, and any deficiency is recorded as a negative number. The weights of these 20 boxes of apples are recorded as follows:

| Difference from Standard Weight (in kilograms) | -2   | -1.5 | -1   | 0    | 1    | 2.5  |
|-----------------------------------------------|------|------|------|------|------|------|
| Number of Boxes                                | 1    | 4    | 2    | 3    | 2    | 8    |

$(1)$ In these 20 boxes of apples, the heaviest box is ______ kilograms heavier than the lightest box;<br/>$(2)$ Find the total weight of these 20 boxes of apples in kilograms;<br/>$(3)$ If the cost price of this type of apple is $5$ yuan per kilogram, and the selling price is $8$ yuan per kilogram, with a loss of 10 kilograms during the selling process. How much yuan can be earned from these 20 boxes of apples?

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