
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 individual operator learned that a boxed product was selling well in the market, so he purchased this product for $40,000. As expected, the product was in high demand after being launched. He then purchased a second batch of this product for $88,000. The quantity purchased in the second batch was twice the quantity purchased in the first batch, but the unit price increased by $4. He priced each box of this boxed product at $56 when selling. The remaining 150 boxes were sold at a discount of 20% and were quickly sold out.  
$(1)$ What were the purchase prices of the boxed product in the two purchases?  
$(2)$ How much profit did this individual operator make in these two transactions?

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