
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, they write three positive integers $p$, $q$, $r$ on three pieces of paper, such that $p < q < r$. When dividing the candy, each person draws a piece of paper, 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 ends up with a total of 20 candy blocks, B with 10 blocks, and C with 9 blocks. It is also known that in the last round, B drew the paper with $r$ on it, and the sum of the numbers on the papers C drew in each round is 18. Find the values of $p$, $q$, and $r$.

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