
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 store sells a type of clothing that costs $45$ yuan to purchase for $65$ yuan. On average, they can sell $30$ pieces per day. In order to reduce inventory quickly, the store decides to take appropriate price reduction measures. A survey found that if the price is reduced by $1$ yuan per piece, they can sell an additional $5$ pieces per day. <br/>$(1)$ If the price of each piece of clothing is reduced by $3$ yuan, then the store can sell ______ pieces per day, and the profit per piece of clothing is ______ yuan. <br/>$(2)$ If the store needs to make a profit of $800$ yuan per day, how much should each piece of clothing be reduced by?

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