
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
The numbers \(1, 2, \ldots, 10\) are written in a circle. There are four people, and each person randomly selects five consecutive integers (e.g. \(1, 2, 3, 4, 5\) or \(8, 9, 10, 1, 2\)). If the probability that there exists some number that was not selected by any of the four people is \(p\), compute \(10000p\).

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