
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 brand of children's clothing in a store in Zhi Li sells two types of clothing, $A$ and $B$, at two stores, Store A and Store B, simultaneously. In April, Store A sold 60 pieces of type $A$ clothing and 15 pieces of type $B$ clothing, with a total sales amount of 3600 yuan. Store B sold 40 pieces of type $A$ clothing and 60 pieces of type $B$ clothing, with a total sales amount of 4400 yuan. <br/>$(1)$ What is the selling price per piece of type $A$ and type $B$ clothing? <br/>$(2)$ In May, it is planned to increase the sales amount of type $A$ clothing by 20%. How much percentage should the sales amount of type $B$ clothing be increased by to make the sales ratio of type $A$ and type $B$ clothing 4:3?

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