
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
Three chiefs of Indian tribes are sitting by a fire with three identical pipes. They are holding a war council and smoking. The first chief can finish a whole pipe in ten minutes, the second in thirty minutes, and the third in an hour. How should the chiefs exchange the pipes among themselves in order to prolong their discussion for as long as possible?

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