
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 handbag, and it is known that the cost price of this handbag is $50$ yuan per unit. Market research shows that the daily sales quantity $y$ (unit: units) of this handbag is related to the selling price $x$ (unit: yuan) as follows: $y=-x+80$ $(50 < x < 80)$. Let $w$ represent the daily sales profit of this handbag.<br/>$(1)$ At what price should the selling price of this handbag be set for the store to maximize its daily sales profit? What is the maximum profit per day?<br/>$(2)$ If the price department stipulates that the selling price of this handbag should not exceed $68$ yuan, and the store needs to make a daily sales profit of $200$ yuan from selling this handbag, what should be the selling price per unit?

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