
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 the rug display featuring sections in three distinct colors, where the areas of these sections form an arithmetic progression, and the width of the center section is 2 feet, and each of the two colored rings around the center section extends outward by 2 feet on all sides, determine the length in feet of the center section.

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