
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
Suppose that $n = 50$, and that the terms of the initial sequence $r_1, r_2, \dots, r_{50}$ are distinct from one another and are in random order. Let $p/q$, in lowest terms, be the probability that the number that begins as $r_{25}$ will end up, after one bubble pass, in the $35^{\mbox{th}}$ place. Find $p + q$.

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