
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

Dodson, Williams, and their horse Bolivar want to reach City B from City A as quickly as possible. Along the road, there are 27 telegraph poles, dividing the whole path into 28 equal intervals. Dodson walks an interval between poles in 9 minutes, Williams in 11 minutes, and either can ride Bolivar to cover the same distance in 3 minutes (Bolivar cannot carry both simultaneously). They depart from City A at the same time, and the journey is considered complete when all three are in City B.

The friends have agreed that Dodson will ride part of the way on Bolivar, then tie Bolivar to one of the telegraph poles, and continue on foot, while Williams will initially walk and then ride Bolivar. At which telegraph pole should Dodson tie Bolivar so that they all reach City B as quickly as possible?

Answer: At the 12th pole, counting from City A.

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