
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
A manager plans to meet three interns at a café. Each of them can arrive randomly between 3:00 and 5:00 p.m. The manager will leave if not all interns are present upon his arrival. Each intern will wait for up to 30 minutes for the others before leaving. What is the probability that the meeting successfully takes place?

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