
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
Travel along the alley clockwise.

In 1 hour of walking, the pedestrian walked 6 kilometers and did not reach point $B$ (a whole $2 \pi - 6$ km!), so the third option is clearly longer than the first and can be excluded.

In the first case, when moving along the alley, they would need to cover a distance of 6 km, and if they move towards each other, the required time is $\frac{6}{6+20}$ hours.

In the second case, when moving towards each other, after $\frac{2 \pi - 6}{6}$ hours, the pedestrian will reach point $B$, and the cyclist will still be riding along the road (since $\frac{4}{15} > \frac{2 \pi - 6}{6}$). Hence, the cyclist will continue to ride along the road until they meet, and the closing speed of the pedestrian and cyclist will be $15 + 6 = 21$ km/h. Therefore, they will meet in $\frac{2 \pi - 2}{21}$ hours.

Let's compare the numbers obtained in the 1st and 2nd cases:

$$
\frac{3}{13} > 0.23 > 0.21 > \frac{2 \cdot 3.15 - 2}{21} > \frac{2 \pi - 2}{21}
$$

(the first and third inequalities can be obtained, for example, by long division). Therefore, the answer is achieved in the 2nd case.

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