
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
Two mathematicians were born in the last 500 years. Each lives between 80 to 120 years. Find the probability that they lived contemporarily (overlapped lives) at any point in time, given each is equally likely to have any specific lifespan within this range and can be born at any time during those 500 years.

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