
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
The price of an item is an integer number of yuan. With 100 yuan, you can buy up to 3 items. Person A and Person B each have a certain number of 100-yuan bills. The amount of money Person A has can buy at most 7 items, and the amount of money Person B has can buy at most 14 items. Together, they can buy 1 more item than the sum of what each can buy individually. What is the price of each item in yuan?

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