
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

During an hour-long walk, the pedestrian traveled 7 kilometers and, passing point \( B \), did not reach point \( A \) by a distance of \( 4 \pi - 7 \) km. Therefore, the first option is definitively longer than the third and can be excluded.

In the third scenario, they need to travel a distance of \( 4 \pi - 7 \) km, and if they move towards each other, the required time is \( \frac{4 \pi - 7}{20 + 7} \) hours.

In the second scenario, when moving towards each other, the pedestrian will reach point \( B \) in \( \frac{7 - 2 \pi}{7} \) hours, while the cyclist will still be on the highway (since \( \frac{4}{15} > \frac{7 - 2 \pi}{7} \)). Thus, the cyclist will be on the highway all the time until meeting the pedestrian, and their relative speed will be \( 15 + 7 = 22 \) km/h. Hence, they will meet in \( \frac{11 - 2 \pi}{22} \) hours.

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

\[ \frac{11 - 2 \pi}{22} > \frac{11 - 2 \times 3.15}{22} > 0.21 > \frac{4 \times 3.15 - 7}{27} > \frac{4 \pi - 7}{27} \]

Therefore, the solution is achieved in the 3rd scenario.

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