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

| Difference from Standard Weight (kg) | -2   | -1.5 | -1   | 0    | 2    | 2.5  | 3    |
|--------------------------------------|------|------|------|------|------|------|------|
| Number of Boxes                      | 3    | 4    | 2    | 2    | 2    | 6    | 1    |

$(1)$ When selecting any two boxes out of the 20, the maximum difference in kilograms between them is ______ $kg$.  
$(2)$ Compared to the standard weight, how many kilograms are the 20 boxes of apples in excess or shortfall by?  
$(3)$ If the cost price of these apples is $6$ yuan per kilogram and the selling price is $8$ yuan per kilogram, how much profit is made in total when all the apples are sold (excluding any damages)?

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