
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 new clothing for seasonal updates, including two styles, $A$ and $B$, totaling 100 pieces, at a cost of 11200 yuan. It is known that the unit price of style $A$ is 120 yuan per piece, and the unit price of style $B$ is 100 yuan per piece.
$(1)$ The store purchased ______ pieces of style $A$ clothing and ______ pieces of style $B$ clothing.
$(2)$ If the selling price of style $A$ is 200 yuan per piece, and the selling price of style $B$ is 140 yuan per piece. If another clothing store also wants to purchase a total of 60 pieces of these two styles of clothing and make a profit of at least 3300 yuan after selling all the purchased clothing, then how many pieces of style $A$ clothing should be purchased at least?

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