
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 rectangular sheet of cardboard was cut along its diagonal. In one of the obtained pieces, 2 cuts were made parallel to the 2 shorter sides and through the midpoints of those sides. In the end, a rectangle with a perimeter of \(129 \, \text{cm}\) remained. What was the perimeter of the sheet before the cut?

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