
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
In the third chapter "Decay Division" of "The Nine Chapters on the Mathematical Art", there is a problem as follows: "Now, person A has 560 money, person B has 350 money, and person C has 180 money. All three people are going through a customs, and the customs duty is 100 money. They want to pay the duty according to the amount of money they have. How much should each person pay?" This means: "Only person A brought 560 money, person B brought 350 money, person C brought 180 money, and the three people together need to pay a total of 100 money in customs duties, according to the amount of money they have, they should pay proportionally." Then, person C should pay $\boxed{17}$ money (round the result to the nearest whole number).

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