
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 cafe with two team members under him. He requests them to arrive between 3:00 and 5:00 p.m. The manager arrives randomly within this time frame as well and waits for up to 30 minutes if at least one team member is present, otherwise, he will leave. Each team member will wait for up to 1.5 hours if the other hasn't appeared by then, before leaving. What is the probability that the meeting actually happens?

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