
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 \( 2018 \times 2018 \) square was cut into rectangles with integer side lengths. Some of these rectangles were used to form a \( 2000 \times 2000 \) square, and the rest were used to form a rectangle whose length differs from its width by less than 40. Find the perimeter of this rectangle.

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