
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 off to go fishing at the lake on foot. Kolya stayed home, promising his friends to meet them on the way back with a bicycle. Vasya was the first to head back home, and at the same time, Kolya set off to meet him on the bicycle. Petya, traveling at the same speed as Vasya, left the lake for home at the moment Vasya and Kolya met. Kolya, after meeting Vasya, immediately turned around and brought Vasya home on the bicycle, then immediately set off again on the bicycle towards the lake. Upon meeting Petya, Kolya once again turned around and brought Petya home. As a result, the time Petya spent traveling from the lake to home was $5 / 4$ of the time Vasya took for the same journey. How much slower would Vasya have been if he walked the entire way home by himself? (8 points)

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