
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. Determine the probability that the number that begins as \( r_{10} \) will end up, after one bubble pass, in the \( 40^{\mbox{th}} \) place. Express your answer as \( p/q \) in lowest terms and find \( p + q \).

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