
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 merchant in Changsha city predicted that a seasonal shirt would sell well in the market, so he purchased a batch of these shirts for $13200. After selling for a period of time, the demand exceeded supply. The merchant then purchased a second batch of these shirts for $28800, with the quantity purchased being twice that of the first batch, but the unit price was $10 higher.  
$(1)$ How many shirts were in the first batch purchased by the merchant?  
$(2)$ If the two batches of shirts are sold at the same price, and the last 50 shirts from the second batch are sold at an 20% discount, with the condition that the overall profit margin after selling all the shirts is not less than 25% (without considering other factors), what is the minimum selling price per shirt?

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