
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 is cut for the first time, removing $\frac{1}{3}$ of its total length. The second time, $30\%$ of the remaining part is cut. If the total length of the removed segments is 0.4 meters more than the remaining part, what is the original length of the rope in meters?

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