
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
When Li Hua was buying a certain product, he misstook the digit "7" in the unit price for a "1," and prepared to pay 189 yuan. The actual amount that should be paid is 147 yuan. Given that both the unit price of the product and the quantity purchased are integers, find the actual unit price of the product (in yuan) and the number of items Li Hua bought.

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