
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 merchant predicted that a type of sportswear would sell well in the market, so he purchased a batch of these sportswear for $12000. After they were launched, they were indeed in short supply. The merchant then purchased a second batch of these sportswear for $26400. The quantity purchased in the second batch was twice that of the first batch, but the cost per item increased by $10.  
$(1)$ Find the number of sportswear items in the second batch purchased by the merchant.  
$(2)$ If both batches of sportswear are sold at a price of $150 per item, what is the total profit after selling all the sportswear?

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