
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 both born in the last 600 years. Each lives (or will live) to be 120 years old, then dies. Each mathematician is equally likely to be born at any point during those 600 years. What is the probability that they were contemporaries for any length of time?

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