
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 workshop in a factory has 50 workers. In a certain month, they received a production task to process two types of car parts. Each worker can process 30 parts of type A or 20 parts of type B per day.  
$(1)$ If a car only needs 7 parts of type A and 2 parts of type B to produce a car set every day, how many workers should be assigned to process type A parts?  
$(2)$ Under the condition in (1), if the cost of processing one part of type A is $10, and the cost of processing one part of type B is $12, and if 50 workers exactly ensure that the parts are processed to produce cars every day, how much is the total processing cost for these 50 workers in one day?

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