
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
A, B, and C are dividing candy blocks in the following way: First, take three identical pieces of paper and write a positive integer $p$, $q$, $r$ on each, such that $p < q < r$. When dividing the candies, each person draws a piece of paper (the paper drawn in the same round is not put back), and then subtracts $p$ from the number on their paper to determine the number of candy blocks they receive in that round. After several rounds of this method, A receives a total of 20 candy blocks, B receives 10, and C receives 9. It is also known that in the last round, B drew the paper with the number $r$, and the sum of the numbers on the papers C drew in each round is 18. The question is: What are the three positive integers $p$, $q$, $r$? Why?

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