
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 clothing store purchased a batch of trendy T-shirts of two types, A and B. Type A cost a total of $9200, while type B cost a total of $6400. The number of type A shirts is twice the number of type B shirts, and the cost price of each type A shirt is $30 less than the cost price of each type B shirt.  
$(1)$ How many shirts of type A and type B were purchased?  
$(2)$ If the store marks up the cost price by $m\%$ to ensure a profit of at least $10920, what is the minimum value of $m$?

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