
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 car parts manufacturing workshop can produce two types of parts, A and B. Producing 4 parts of type A and 3 parts of type B yields a profit of $120. Producing 2 parts of type A and 5 parts of type B yields a profit of $130.  
$(1)$ Find the profit of producing 1 part of type A and 1 part of type B, respectively.  
$(2)$ If the workshop has a total of 30 workers, each worker can produce 6 parts of type A or 5 parts of type B per day, and each worker can only produce one type of part per day. To ensure that the total profit from producing the two types of parts exceeds $2800 per day, how many workers at least should be assigned to produce type B parts?

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