
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 certain clothing factory plans to produce 2800 sets of sportswear in a week, with an average daily production plan of 400 sets. Production exceeding the planned quantity is denoted as "$+$", while production below the planned quantity is denoted as "$-$". The table below records the production situation of the factory for a week, with the record for Saturday being accidentally stained with ink.

| Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday | Total |
|--------|---------|-----------|----------|--------|----------|--------|-------|
| $+15$  | $-5$    | $+21$     | $+16$    | $-7$   |          | $-8$   | $+80$ |

$(1)$ According to the records, how many sets of sportswear were produced on Saturday by the factory?  
$(2)$ How many more sets of sportswear were produced on the day with the highest production compared to the day with the lowest production?  
$(3)$ The wage settlement method of the clothing factory is as follows:  
① Basic daily wage per person is $200$ yuan.  
② Based on a daily completion of 400 sets, if the daily production exceeds the target, an additional $10$ yuan per set is rewarded; if the daily production falls short, a deduction of $15$ yuan is made for each set less produced. The bonus earned on that day is distributed equally among the workers. If the factory has 20 workers producing each day for a week, how much should each worker be paid by the factory for that week?

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