
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
Zhao Tong apples and Tianma from Xiaocaoba are delicious. Xiao Ming needs to pay 105 yuan for 1 jin of Zhao Tong apples and 2 jin of Tianma from Xiaocaoba at a supermarket in Kunming. He needs to pay 265 yuan for 3 jin of Zhao Tong apples and 5 jin of Tianma from Xiaocaoba. <br/> $(1)$ What are the unit prices of 1 jin of Zhao Tong apples and 1 jin of Tianma from Xiaocaoba? <br/> $(2)$ The distance from Kunming to Zhao Tong is about 350 km. In the past, the supermarket owner would personally go to Zhao Tong to select fruits, but due to this year's epidemic, they can only choose a special car for transportation. The apples that used to cost 240 yuan now cost 300 yuan. The purchase price has increased by 1 yuan. What was the original purchase price of 1 jin of apples?

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