
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 supermarket offers discounts on two types of products, A and B. Product A is discounted by 20%, and product B is discounted by 25%. It is known that before the discount, buying 6 units of product A and 3 units of product B costs $600. After the discount, buying 50 units of product A and 40 units of product B costs $5200.  
$(1)$ What is the price of each unit of product A and product B before the discount?  
$(2)$ If a person buys 80 units of product A and 100 units of product B, how much money can be saved by buying these products after the discount compared to not having any discount?

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