
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 30 boxes of apples, with a standard weight of 20 kilograms per box. The excess or shortfall in kilograms is represented by positive or negative numbers, as shown below:

| Difference from Standard Weight (kg) | $-1.5$ | $-1$ | $-0.5$ | $1$ | $2$ |
|--------------------------------------|--------|------|--------|-----|-----|
| Number of Boxes                      | $2$    | $6$  | $10$   | $8$ | $4$ |

$(1)$ In these 30 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 these 30 boxes of apples exceed or fall short of in total?  
$(3)$ If the selling price of apples is $6$ yuan per kilogram, how much can these 30 boxes of apples be sold for?

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