
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
The 24th Winter Olympics, the 2022 Beijing Winter Olympics, is scheduled to open on Friday, February 4, 2022, and close on Sunday, February 20, 2022. The emblem and mascots of the Winter Olympics have been successively released. A public welfare team plans to contact the Winter Olympics Organizing Committee to hold a one-month online commemorative product exhibition and sale, with all profits used for the construction of community sports facilities. According to market research, the daily sales volume $y$ (unit: pieces) of a certain commemorative product is a linear function of the selling price $x$ (unit: yuan/piece), and the higher the price, the lower the sales volume. When the price is equal to or higher than 110 yuan/piece, the sales volume is 0. It is known that the cost price of this commemorative product is 10 yuan/piece, and the exhibition requires selling the product at a price higher than the cost price.

$(1)$ If you want to maximize the daily profit of this commemorative product, what should be the price per piece?

$(2)$ Usually, achieving the maximum daily profit for a product is just an "ideal result." If you want to achieve 84% of the maximum daily profit for this commemorative product, what should be the price per piece?

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