
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
"Passion for Ice and Snow, Moving towards the Future", the Beijing Winter Olympics arrived as scheduled on February 4, 2022. A certain business seized the opportunity and started selling souvenirs of the Winter Olympics mascot "Bing Dwen Dwen". The cost price of each souvenir is 40 yuan. It is stipulated that the selling price should not be less than 44 yuan and not more than 60 yuan. During the sales period, it was found that when the selling price was set at 44 yuan, 300 units could be sold per day. Due to the hot sales, the business decided to increase the price. After market research, it was found that for every 1 yuan increase in selling price, the daily sales volume decreased by 10 units.<br/>$(1)$ Find the selling price per souvenir at which the business makes a daily profit of 2640 yuan;<br/>$(2)$ At what price should the selling price of the souvenir be set so that the business maximizes the profit earned from selling souvenirs per day? What is the maximum profit?

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