
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
With the popularity of smartphones, many people have started doing "e-commerce," and many agricultural products have also changed their original sales models and implemented online sales. Xiao Liang, who has just graduated from college, put his family's sweet potato products for sale online. He originally planned to sell $100$ kilograms per day. Due to various reasons, the actual daily sales volume deviates from the planned amount. The table below shows the sales situation during the National Day holiday (excess is recorded as positive, shortfall as negative, unit: kilograms):

| Time | 1st day | 2nd day | 3rd day | 4th day | 5th day | 6th day | 7th day |
|------|---------|---------|---------|---------|---------|---------|---------|
| Deviation from Planned Amount | $+8$ | $-2$ | $+17$ | $+22$ | $-5$ | $-8$ | $-3$ |

$(1)$ According to the table above, how many kilograms were sold in the first three days in total?  
$(2)$ How many kilograms more were sold on the day with the highest sales compared to the day with the lowest sales?  
$(3)$ If each kilogram is sold for $2.5$ yuan and an average shipping cost of $0.5$ yuan per kilogram is required, how much money did Xiao Liang earn during the National Day holiday?

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