
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 craft, with a cost of $30$ yuan per item. In order to set a reasonable price, the craft is put on the market for trial sales. According to market research, when the selling price is $40$ yuan, the daily sales volume is 80 items. For every $1$ yuan increase in the selling price, there is a decrease of 2 items sold per day. However, the selling price must not exceed $55$ yuan.  
$(1)$ If the selling price is $45$ yuan per item, find the daily sales profit.  
$(2)$ To make a profit of $1200$ yuan per day from selling this craft, what should be the selling price per item?

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