
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 to meet with two engineers at a coffee shop. Each person arrives randomly between 3:00 PM and 5:00 PM. If the boss arrives and does not find both engineers, he will immediately leave. Each engineer is willing to wait for up to 1.5 hours for the other. If an engineer arrives at least 30 minutes before the other, he will leave if the second engineer hasn't arrived within 1.5 hours of the first's arrival. What is the probability that the meeting occurs?

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