
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
In a certain region, smart classrooms are supported by mobile internet and big data technology to achieve students' autonomous, personalized, and diversified learning. All students in the region gradually use tablets for all classes. A certain shopping mall purchased type A tablets for $60,000 and quickly sold out. The mall then purchased type B tablets for $128,000, with the quantity purchased being twice that of type A tablets, but the unit price was $40 higher. Both type A and type B tablets were sold for $700 each. However, the remaining 50 type B tablets were sold at an 20% discount and were quickly sold out.  
$(1)$ What were the unit prices of type A and type B tablets purchased by the mall?  
$(2)$ How much profit did the mall make after selling these two types of tablets?

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