
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 bike-sharing company in a city plans to order 2100 bicycles to be put into the city. The bike factory plans to complete the production in one week, with an average daily production of 300 bicycles. Due to various reasons, the actual daily production varies from the planned amount. The table below shows the production situation for a week (positive numbers indicate overproduction, negative numbers indicate underproduction):

| Day of the Week | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
|-----------------|--------|---------|-----------|----------|--------|----------|--------|
| Production Deviation (bicycles) | +6 | -2 | -3 | +14 | -10 | +8 | -9 |

$(1)$ According to the records, how many bicycles were produced in the first three days?

$(2)$ How many bicycles were produced on the day with the least production? How many more bicycles were produced on the day with the most production compared to the day with the least production?

$(3)$ The factory implements a piece-rate wage system, with $60$ yuan per bicycle. For exceeding the task, an additional $15$ yuan is awarded for each bicycle produced beyond the target, while a deduction of $15$ yuan is made for each bicycle produced below the target. What is the total wage of the factory workers for the week?

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