
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 $s_1, s_2, ..., s_{50}$ of distinct real numbers ordered randomly. Each number can be sorted into ascending order through one or more bubble passes, where each bubble pass involves comparing and potentially swapping adjacent numbers if the latter is smaller. Consider $s_{30}$ and determine the probability that, after one bubble pass, it occupies the $40^{th}$ position. Assume the sequence is such that the starting position can move only during the comparison if the required conditions are met.

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