
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 two assistants at a café. The manager forgets to set a specific time for the meeting, so they each independently decide to arrive at some random time between 3:00 PM and 5:00 PM. The manager will leave immediately if both assistants are not present when he arrives. The first assistant will wait for up to 45 minutes for the others, while the second assistant is willing to wait for up to 90 minutes. What is the probability that the meeting successfully takes place?

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