
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
Alyosha and Vitia are traveling from point \(N\) to point \(M\), with a distance of 20 km between the points. Unfortunately, they have only one bicycle to share. Alyosha starts from \(N\) on the bicycle while Vitia walks. Alyosha can leave the bicycle at any point along the road and continue on foot. When Vitia reaches that point, he will take the bicycle. Alyosha's walking speed is 4 km/h, and his cycling speed is 15 km/h. Vitia's walking speed is 5 km/h, and his cycling speed is 20 km/h. At which point should Alyosha leave the bicycle so that both arrive at \(M\) simultaneously?

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