
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 with three team members at a coffee shop but forgets to specify a time. Each person arrives randomly between 3:00 PM and 5:00 PM. The manager will leave if not all team members are already there. Each team member waits for exactly 30 minutes and will leave if others haven't arrived by then. What is the probability that the meeting will successfully take place?

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