
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
As the Spring Festival approaches, fruits continue to sell well. A fruit merchant purchased the first batch of 30 boxes of Ponkan oranges and 20 boxes of Fuji apples, spending a total of 2700 yuan, all of which were sold out. The cost of the second batch of 50 boxes of Ponkan oranges and 40 boxes of Fuji apples was 4800 yuan.<br/>$(1)$ Please calculate the cost per box of Ponkan oranges and Fuji apples.<br/>$(2)$ The fruit merchant sells Ponkan oranges for 80 yuan per box and Fuji apples for 60 yuan per box. After selling 50 boxes of Ponkan oranges and 20 boxes of Fuji apples quickly, the fruit merchant reduces the price of Fuji apples by 10%. After selling 10 boxes at the reduced price, the fruit merchant further reduces the price of Fuji apples by 10% to sell the remaining boxes. What is the profit obtained by the fruit merchant from selling the second batch of fruits?

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