
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 piece of clothing costs $80$ yuan to purchase and is sold for $120$ yuan, resulting in the sale of $30$ pieces per day. A market survey reveals that if the price of each piece of clothing is reduced by $1$ yuan, then an additional $3$ pieces can be sold on average per day. Let the price reduction per piece of clothing be $x$ yuan.  
$(1)$ The daily increase in sales is ______ pieces, and the profit per piece of clothing is ______ yuan (expressed as an algebraic expression involving $x$);  
$(2)$ In a scenario where the business is offering discounts to customers, how much should the price of each piece of clothing be reduced by for the business to make an average daily profit of $1800$ yuan?

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