
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 bicycle factory plans to produce 1400 bicycles in a week, with an average daily production of 200 bicycles. However, due to various reasons, the actual daily production deviates from the planned quantity. The table below shows the production situation for a week (positive values indicate overproduction, negative values indicate underproduction):

| Day of the Week | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
|-----------------|--------|---------|-----------|---------|--------|----------|--------|
| Production Deviation | +5 | -2 | -4 | +13 | -10 | +16 | -9 |

$(1)$ Based on the recorded data, how many bicycles were actually produced by the factory this week?  
$(2)$ The factory pays its workers based on the actual daily production. For each bicycle produced, the worker receives $60. If the production exceeds the target, an additional $15 is awarded for each extra bicycle. What is 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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