
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
Three engineers plan to meet at a café for a discussion. Each arrives at a random time between 3:00 PM and 5:00 PM. If the first engineer to arrive does not see the other two within 30 minutes, he will leave. What is the probability that all three engineers meet?

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