
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
Alice and Bob are each secretly given a real number between 0 and 1 uniformly at random. Alice states, “My number is probably greater than yours.” Bob repudiates, saying, “No, my number is probably greater than yours!” Alice concedes, muttering, “Fine, your number is probably greater than mine.” If Bob and Alice are perfectly reasonable and logical, what is the probability that Bob’s number is actually greater than Alice’s?

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