
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
Given a line segment of length $1$, divide it into three equal parts, remove the middle segment, leaving the remaining two segments, and repeatedly continue this operation, with each operation reducing the lengths of the remaining segments, calculate the maximum value of $n$ for which the total length of the removed segments is not less than $\frac{1}{60}$.

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