
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 6.5 kilometers in 1 hour and, after passing point $B$, did not reach point $A$ by $4\pi - 6.5$ km. 

In the third scenario, they travel along the alley covering a distance of $4\pi - 6.5$ km. If they are moving towards each other, the required time is $\frac{4\pi - 6.5}{20 + 6.5}$ hours.

In the second scenario, moving towards each other, the pedestrian will reach point $B$ after $\frac{6.5 - 2\pi}{6.5}$ hours, while the cyclist will still be on the road (since $\frac{4}{15} > \frac{6.5 - 2\pi}{6.5}$). The cyclist will be on the road all the time, and the relative speed of approach will be $15 + 6.5 = 21.5$ km/h. Hence, they will meet after $\frac{10.5 - 2\pi}{21.5}$ hours.

Compare the times obtained in the 2nd and 3rd scenarios:

$$
\frac{10.5 - 2\pi}{21.5} < \frac{21 - 4 \cdot 3.14}{43} < 0.20 < 0.22 < \frac{8 \cdot 3.14 - 13}{53} < \frac{4 \pi - 6.5}{26.5}
$$

Therefore, the answer is in the 2nd scenario.

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