
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
An electric cable of length 21 meters is cut into 21 pieces. For any two pieces, their lengths differ by no more than a factor of three. What is the smallest value of \(m\) for which there must be two pieces whose lengths differ by no more than \(m\) times?

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