
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
Three mathematicians were each born within the last 600 years. Each lives to be 120 years old and then dies. Each mathematician is equally likely to be born at any point during those 600 years. What is the probability that at least two of them were contemporaries for any length of time?

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