
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, Alice and Bob, were each born in the last 600 years. Each lives to be 120 years old. Each mathematician has an equal likelihood of being born at any point during those 600 years. Determine the probability that they lived during the same period at any point in time.

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