
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
Petya and Vasya simultaneously set off on scooters towards each other. There is a bridge exactly in the middle between them. The road from Petya to the bridge is paved, while the road from Vasya to the bridge is dirt. It is known that they travel at the same speeds on the dirt road, but Petya moves 3 times faster on the paved road than on the dirt road. Petya reached the bridge in one hour and continued moving without stopping. How much time after starting will Petya meet Vasya?

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