
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 purchasing officer at a certain shopping mall predicted that a certain seasonal $T$-shirt would sell well in the market, so he purchased a batch of these $T$-shirts for $4000$ yuan. After they were put on the market, they were indeed in short supply. The mall then purchased a second batch of these $T$-shirts for $8800$ yuan, with the quantity purchased being twice that of the first batch, but the cost price of each item was $4$ yuan more expensive.  
$(1)$ What is the cost price per item for the first and second batches of $T$-shirts purchased by the mall?  
$(2)$ If the two batches of $T$-shirts are sold at the same retail price, and the remaining 40 $T$-shirts are sold at a 30% discount to ensure that all the $T$-shirts are sold out and the profit margin is not less than 80% (without considering other factors), what is the minimum retail price per item for the $T$-shirts?

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