
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
Dotson, Williams, and their horse Bolivar want to get from city A to city B as quickly as possible. There are 27 telegraph poles along the road, dividing the entire route into 28 equal segments. Dotson walks between the poles in 9 minutes, Williams in 11 minutes, and riding Bolivar, either of them covers the distance in 3 minutes (Bolivar can't carry both). They start from city A at the same time; the journey is considered complete when everyone reaches city B.

The friends agreed that Dotson would ride part of the way on Bolivar, then tie Bolivar to one of the telegraph poles and walk the rest of the distance. Meanwhile, Williams would initially walk and then ride Bolivar. At which pole should Dotson tie Bolivar so that they complete the journey to city B as quickly as possible?

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