
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
There are 15 boxes of apples, with a standard weight of 25kg per box. The excess or shortfall is represented by positive or negative numbers, as shown in the table below. Please answer the following questions:

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

$(1)$ In the 15 boxes of apples, how many kilograms heavier is the heaviest box compared to the lightest box?  
$(2)$ Compared to the standard weight, how many kilograms do the total weight of the 15 boxes of apples exceed or fall short of?  
$(3)$ If the selling price of apples is $8$ yuan per kilogram, how much profit can be made by selling all 15 boxes of apples?

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