
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
Paul and Caroline arranged to meet under the Arc de Triomphe between 11 AM and noon. Each of them will arrive at a random time within this interval. According to their agreement, if the other person does not appear within fifteen minutes, the first one to arrive will not wait any longer.

What is the probability that Paul and Caroline will meet?

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