
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 craft factory plans to produce 2100 handicrafts in a week, with an average daily production of 300. However, the actual daily production deviates from the plan. The table below shows the production situation for a week (positive for overproduction and negative for underproduction):

| Day of the Week | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
|-----------------|--------|---------|-----------|----------|--------|----------|--------|
| Production Deviation (units) | +5 | -2 | -5 | +15 | -10 | +16 | -9 |

$(1)$ Write down the number of handicrafts produced by the factory on Monday.  
$(2)$ How many more handicrafts were produced on the day with the highest production compared to the day with the lowest production this week?  
$(3)$ Calculate the actual number of handicrafts produced by the factory this week.  
$(4)$ It is known that the factory implements a piece-rate wage system, where each handicraft produced earns $60. If the task is completed in excess, an additional $50 is awarded for each excess item, and a penalty of $80 is imposed for each item produced less. Calculate the total wage the factory should pay out this week.

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