
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

Friends Vasya, Petya, and Kolya live in the same house. One day, Vasya and Petya set out on foot to go fishing at the lake. Kolya stayed home but promised to meet his friends on the way back on his bicycle. Vasya was the first to head home, and at the same time, Kolya set out on his bicycle to meet him. Petya started his journey home from the lake with the same speed as Vasya at the moment when Kolya and Vasya met. Kolya, upon meeting Vasya, immediately turned around and gave him a ride home on his bicycle. Then, Kolya set off again on his bicycle towards the lake to meet Petya. After meeting Petya, Kolya turned around once more and took him home. As a result, the time Petya spent traveling from the lake to home was $4 / 3$ of the time Vasya spent on the same journey. How many times slower would Vasya's journey be to get home if he had walked the entire way? (8 points)

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