
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 a sequence $s_1, s_2, \dots, s_{50}$ of distinct real numbers is randomly ordered. A single bubble pass is applied to this sequence. Determine the probability, in its simplest form, that the number initially at position $s_{25}$ ends up in position $35$ after one bubble pass. Let the probability be expressed as $p/q$ in lowest terms and find $p + q$.

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