
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
Consider two mathematicians, Ada and Grace, each of whom lived or are to live precisely 80 years within a span of 800 years. They are equally likely to be born at any time during these 800 years. Determine the probability that Ada and Grace were alive at the same time for any duration.

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