
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 friends agree to meet at a specific place between 12:00 PM and 12:30 PM. The first one to arrive waits for the other for 20 minutes before leaving. Find the probability that the friends will meet, assuming each chooses their arrival time randomly (between 12:00 PM and 12:30 PM) and independently.

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