
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
A rope of 1 meter long is cut by $\frac{2}{3}$ for the first time, then the remaining is cut by $\frac{2}{3}$ again, and so on. The length of the rope left after the fourth cut is ______ meters, and the length left after the $n$th cut is ______ meters.

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