
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 large supermarket purchasing officer predicted that a certain health drink would sell well in the market, so he purchased the first batch of this health drink for $40,000. After it was launched, it was indeed in short supply. The supermarket then purchased the second batch of this health drink for $88,000, with the quantity purchased being twice that of the first batch, but the unit price increased by $2.<br/>$(1)$ How many bottles of the first batch of health drink were purchased?<br/>$(2)$ If the supermarket priced each bottle of this health drink at $28, and the remaining 100 bottles were sold at a 20% discount, and were quickly sold out. How much profit did the supermarket make from selling these two batches of health drink?

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