
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 shopping mall has a certain number of $A$ and $B$ styles of T-shirts. The total cost of $A$ style T-shirts is 1200 yuan, and the total cost of $B$ style T-shirts is 6000 yuan. The cost price of each $B$ style T-shirt is 80 yuan higher than that of each $A$ style T-shirt, and the quantity of $B$ style T-shirts is exactly 3 times the quantity of $A$ style T-shirts.  
$(1)$ Find the cost prices of the first purchase of $A$ and $B$ style T-shirts.  
$(2)$ After the first batch of goods is sold out, the mall decides to purchase a certain number of $B$ style T-shirts again, with a total purchase quantity not exceeding 60 pieces. The sales situation of the mall is as follows: 15 pieces are sold at the standard price of 300 yuan, and the remaining pieces are sold at a 20% discount off the standard price. If the total profit is not less than 3220 yuan, find how many pieces of $B$ style T-shirts can be purchased in the second purchase.

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