
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 rug is designed with three colors, creating three distinct rectangular regions. The areas of these regions form an arithmetic progression. The innermost rectangle has a width of 2 feet, and each of the two shaded regions surrounding it is 2 feet wide on all sides. Find the length in feet of the innermost rectangle.

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