
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
Red Star Company wants to recruit 150 workers for two types of jobs, A and B. The monthly wages for workers in types A and B are 2000 yuan and 3000 yuan, respectively. It is required that the number of workers in type B should be at least twice the number of workers in type A. How many workers of type A should be recruited to minimize the monthly wage paid by the company? What is the minimum monthly wage paid by the company in this case?

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