
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 pedestrian walked 5.5 kilometers in 1 hour but did not reach point \( B \) (short by \(2 \pi - 5.5\) km). Therefore, the third option is longer than the first and can be excluded.

In the first case, they need to cover a distance of 5.5 km along the alley. If they move towards each other, the required time is \(\frac{5.5}{20 + 5.5}\) hours.

In the second case, moving towards each other, after \(\frac{2 \pi - 5.5}{5.5}\) hours the pedestrian will reach point \( B \), while the cyclist will still be riding on the highway (since \(\frac{4}{15} > \frac{2 \pi - 5.5}{5.5}\)). Thus, the cyclist will always be on the highway and the closing speed of the pedestrian and the cyclist will be \(15 + 5.5 = 20.5\) km/h. They will meet in \(\frac{2 \pi - 1.5}{20.5}\) hours.

Compare the numbers obtained in cases 1 and 2:

$$
\frac{5.5}{25.5} = \frac{11}{51} < 0.22 < 0.23 < \frac{4 \cdot 3.14 - 3}{41} < \frac{2 \pi - 1.5}{20.5}
$$

Therefore, the answer is given by the first case.

**Note**: Some participants interpreted the condition differently, considering that the pedestrian and the cyclist met after an hour, and at that time, the pedestrian asked the cyclist to bring him the keys. Since the condition does not specify where exactly the neighbor was, and with a different interpretation of the condition, a similar problem arises (although with slightly more cumbersome calculations), the jury decided to accept both interpretations of the condition. The plan for solving the second interpretation is provided.

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