
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 shopping mall purchased two types of goods, A and B. The total cost for type A goods was $2000, and for type B goods was $2400. It is known that the cost price per unit of type B goods is $8 more than that of type A goods, and the quantities of type A and type B goods purchased are the same.  
$(1)$ Find the cost price per unit of type A and type B goods.  
$(2)$ The shopping mall sells the purchased type A and type B goods. The selling price per unit of type A goods is $60, and for type B goods is $88. During the sales process, it was found that the sales volume of type A goods was not good. The mall decided that after selling a certain quantity of type A goods at the original selling price, the remaining type A goods would be sold at a 30% discount off the original selling price, while the selling price of type B goods remained unchanged. To ensure a total profit of at least $2460 after selling all the goods, how many units of type A goods should be sold at the original selling price at least?

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