
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
A fruit farmer packages strawberries from his own orchard before selling them. The original plan was to sell $10$ boxes per day, but due to various reasons, the actual daily sales volume varied from the planned amount. The table below shows the sales situation for a week (positive for exceeding the plan and negative for falling short, unit: boxes):

| Day of the Week | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
|-----------------|--------|---------|-----------|----------|--------|----------|--------|
| Difference from Planned Amount | $+4$ | $-3$ | $-2$ | $+7$ | $-6$ | $+18$ | $-5$ |

$(1)$ According to the table, the day with the highest sales volume sold ______ more boxes than the day with the lowest sales volume;<br/> 
$(2)$ How many boxes did the actual sales volume exceed or fall short of the planned quantity for the week? Please explain your reasoning through calculations;<br/> 
$(3)$ If the selling price of each box of strawberries is $65$ yuan, and it is known that the orchard has $3$ workers, with daily expenses of $80$ yuan per person, and a packaging fee of $5$ yuan per box sold, how much profit did the farmer make this week?

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