
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 students agreed to meet at a specific place between 12:00 PM and 1:00 PM. The one who arrives first will wait for the other for $\alpha$ minutes ($\alpha < 60$) before leaving. What is the probability of their meeting (event $A$) if the arrival time of each of them can occur randomly within the specified hour, with the arrival times being independent? Consider the special case where $\alpha = 10$ minutes.

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