
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 schedules a meeting at a coffee shop with two assistants. Due to a misunderstanding, he does not specify a meeting time, and all three of them decide to arrive randomly between 12:00 and 4:00 p.m. If the manager arrives and any assistant is not there, he will wait for a maximum of 30 minutes before leaving. Each assistant will wait for only 30 minutes if the other assistant has not arrived by then, after which they will leave. What is the probability that the meeting actually takes place?

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