
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 stationery store owner went to a wholesale market to purchase sets of drawing tools from two brands, $A$ and $B$. The cost price of each set of brand $A$ is $2.5$ yuan more than the cost price of each set of brand $B$. It is known that the quantity of brand $A$ sets purchased for 200 yuan is twice the quantity of brand $B$ sets purchased for 75 yuan.

(1) Find the cost price per set of brand $A$ and brand $B$.

(2) If the selling price per set of brand $A$ is 13 yuan and brand $B is 9.5 yuan, the store owner decides to purchase 4 more sets of brand $B$ than twice the quantity of brand $A$. After selling all the sets, to make a profit exceeding 120 yuan, how many sets of brand $A$ should be purchased at least?

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