
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 baskets of Chinese cabbage, with a standard weight of 25 kilograms per basket. The excess or shortfall in kilograms is represented by positive or negative numbers, as shown below:

| Difference from Standard Weight (kg) | $-3$ | $-2$ | $-1$ | $0$ | $1$ | $2$ |
|--------------------------------------|------|------|------|----|----|----|
| Number of Baskets                     | $1$  | $4$  | $2$  | $3$| $2$| $8$|

$(1)$ In the 20 baskets of Chinese cabbage, how many kilograms heavier is the heaviest basket compared to the lightest basket?  
$(2)$ Compared to the standard weight, how many kilograms do the 20 baskets of Chinese cabbage exceed or fall short of in total?  
$(3)$ If the cost price of Chinese cabbage is $1.6$ yuan per kilogram and the selling price is $2$ yuan, how much profit can be made by selling these 20 baskets of Chinese cabbage?

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