
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
Vasya and Petya simultaneously started running from the starting point of a circular track in opposite directions at constant speeds. At some point, they met. Vasya completed a full lap and, continuing to run in the same direction, reached the point of their first meeting at the same moment Petya completed a full lap. Find the ratio of Vasya's speed to Petya's speed.

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