
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 $s_1, s_2, \dots, s_{35}$ of distinct real numbers in random order. A single bubble pass is performed on this sequence. Let the probability that the number initially at $s_{15}$ moves to the $25^{\mbox{th}}$ position after one bubble pass be expressed as $p/q$, where $p$ and $q$ are coprime integers. Determine the value of $p + q$.

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