
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

At the moment when Pierrot left the "Commercial" bar, heading to the "Theatrical" bar, Jeannot was leaving the "Theatrical" bar on his way to the "Commercial" bar. They were walking at constant (but different) speeds. When the vagabonds met, Pierrot proudly noted that he had walked 200 meters more than Jeannot. After their fight ended, they hugged and continued on their paths but at half their previous speeds due to their injuries. Pierrot then took 8 minutes to reach the "Theatrical" bar, and Jeannot took 18 minutes to reach the "Commercial" bar. What is the distance between the bars?

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