
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
Xiao Zhang went to work at a certain factory. After entering the factory, Xiao Zhang found that it takes 5 hours to process 1 part of type $A$ and 3 parts of type $B$, and it takes 9 hours to process 2 parts of type $A$ and 5 parts of type $B$. <br/>Salary: working 8 hours a day, working 25 days a month, processing 1 part of type $A$ earns 16 yuan, and processing 1 part of type $B$ earns 12 yuan. Monthly salary = base salary (800 yuan) + piecework wages. <br/>$(1)$ How many hours does Xiao Zhang need to process 1 part of type $A$ and 1 part of type $B$ respectively? <br/>$(2)$ If the company stipulates that Xiao Zhang must process no less than 50 parts of type $A$ per month, how many parts of type $A$ and type $B$ should Xiao Zhang process each month to earn the maximum salary? How much is the maximum salary?

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