
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

Two candidates participated in an election with \(p+q\) voters. Candidate \(A\) received \(p\) votes and candidate \(B\) received \(q\) votes, with \(p > q\). During the vote counting, only one vote is registered at a time on a board. Let \(r\) be the probability that the number associated with candidate \(A\) on the board is always greater than the number associated with candidate \(B\) throughout the entire counting process.

a) Determine the value of \(r\) if \(p=3\) and \(q=2\).

b) Determine the value of \(r\) if \(p=1010\) and \(q=1009\).

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