
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
Technology changes life, and online sales are becoming increasingly popular. Many agricultural businesses use online sales to market their products and achieve prosperity. Xiao Hong sells the apples grown in her own home online, planning to sell $100$ kilograms per day. The actual daily sales volume varies compared to the planned sales volume, with exceeding the planned amount recorded as positive and falling short of the planned amount recorded as negative. The table below shows the sales situation of Xiao Hong's fruit in the first week:

| Day of the Week | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
|-----------------|--------|---------|-----------|----------|--------|----------|--------|
| Excess or Shortage of Apple Sales (in kilograms) | $+7$ | $-5$ | $-3$ | $+13$ | $-6$ | $+12$ | $+5$ |

$(1)$ How many kilograms more apples did Xiao Hong sell on the day with the highest sales compared to the day with the lowest sales in the first week?<br/>
$(2)$ How many kilograms of apples did Xiao Hong actually sell in total in the first week?<br/>
$(3)$ If Xiao Hong sells apples at $5.5$ yuan per kilogram (including postage) and bears an average shipping cost of $2$ yuan per kilogram, how much revenue did Xiao Hong earn from selling apples in the first week?

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