
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
Anya, Borya, and Vasya decided to go to the "Christmas Tree" event. They agreed to meet at the bus stop but do not know when each will arrive. Each of them can arrive at any random moment between 3:00 PM and 4:00 PM. Vasya is the most patient: if he arrives and neither Anya nor Borya is there, he will wait for 15 minutes. If no one arrives within that time, he will go to the "Christmas Tree" alone. Borya is less patient: he will wait only 10 minutes. Anya is the least patient: she will not wait at all. However, if Borya and Vasya meet, they will wait for Anya until 4:00 PM. What is the probability that all three will go to the "Christmas Tree" together?

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