
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 electric car factory plans to produce 2100 electric cars in a week, with an average daily production plan of 300 cars. Due to various reasons, the actual daily production varies from the planned quantity. 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 | +5 | -2 | -4 | +13 | -10 | +16 | -9 |

$(1)$ How many more cars were produced on the day with the highest production compared to the day with the lowest production?  
$(2)$ According to the records, how many cars were produced in total this week?  
$(3)$ The factory implements a piece-rate wage system every week, where each electric car produced earns $a$ dollars. If the production exceeds the target, an additional $b$ dollars is awarded for each car in excess $(b < a)$. If the production falls short by one car, $b$ dollars are deducted. Find the total wage of the workers in the factory for this week.

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