
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
Consider a sequence $s_1, s_2, \dots, s_{50}$ of distinct real numbers in a random order. We apply a "bubble pass" through this sequence. Let $s_{25}$ originally be at the 25th position. Find the probability that after one bubble pass, $s_{25}$ ends up in the $40^{\text{th}}$ place. Assume each number is distinct and randomly placed initially. Express your answer as $p/q$, where $p$ and $q$ are coprime integers, and find $p + q$.

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