
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 boss plans a business meeting at a local café with three engineers below him. All four individuals randomly arrive at the café anytime between 1:00 and 3:00 p.m. The boss, upon arriving, will only stay if all three engineers are already there; otherwise, he will leave immediately. Each engineer can wait at the café for up to 30 minutes for the others before leaving. Determine the probability that the meeting successfully takes place.

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