
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 in a sequence $r_1, r_2, \dots, r_{50}$ of distinct real numbers in random order, $n = 50$, and the terms of the initial sequence are distinct. We perform one bubble pass. What is the probability, in simplest form, that the number starting at position $r_{25}$ ends up, after this bubble pass, in the $35^{\mbox{th}}$ position? Calculate $p + q$ where the probability is expressed as $p/q$.

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