
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 factory plans to produce 700 toys in a week, with an average daily production of 100 toys. Due to various reasons, the actual daily production deviates from the planned quantity. The table below shows the daily production situation for a week (positive for increased production, negative for decreased production, unit: toys):

| Day of the Week | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
|-----------------|--------|---------|-----------|----------|--------|----------|--------|
| Production      | +10    | -6      | -8        | +15      | -12    | +18      | -9     |

$(1)$ According to the records, how many toys were produced in the first three days?
$(2)$ How many more toys were produced on the day with the highest production compared to the day with the lowest production?
$(3)$ The factory implements a piece-rate wage system, with $10$ yuan paid for each toy produced. If the weekly production target is exceeded, an additional $12$ yuan is paid for each toy produced beyond the target. If the target is not met, each toy produced is paid only $8$ yuan. What is the total wage for the factory workers for this week?

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