
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 group of schoolchildren arrived at a camp, among them Petya, Vasya, and Timofey, who were not acquainted with each other but each had acquaintances among the other children. Petya noticed that exactly \( \frac{1}{2} \) of his acquaintances are acquainted with Vasya, and exactly \( \frac{1}{7} \) are acquainted with Timofey. Vasya noticed that \( \frac{1}{3} \) of his acquaintances are acquainted with Petya, and \( \frac{1}{6} \) are acquainted with Timofey. Finally, Timofey noticed that exactly \( \frac{1}{5} \) of his acquaintances are acquainted with Petya. What fraction of Timofey's acquaintances are also acquainted with Vasya?

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