
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
On the eve of the Dragon Boat Festival, a supermarket purchased egg yolk zongzi and red bean zongzi from the manufacturer twice. The purchase price of the two types of zongzi remained the same for both purchases. The first purchase included 60 bags of egg yolk zongzi and 90 bags of red bean zongzi, totaling 4800 yuan. The second purchase included 40 bags of egg yolk zongzi and 80 bags of red bean zongzi, totaling 3600 yuan.  
$(1)$ Find the purchase price per bag of egg yolk zongzi and red bean zongzi.  
$(2)$ When the selling price of egg yolk zongzi is 70 yuan per bag, 20 bags can be sold per day. In order to promote sales, the supermarket decides to reduce the price of egg yolk zongzi. According to market research, if the selling price per bag is reduced by 1 yuan, the daily sales volume will increase by 5 bags. At what price per bag should the egg yolk zongzi be sold so that the profit from selling egg yolk zongzi per day is 220 yuan?

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