
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 different colors as illustrated. The areas of the three differently colored regions form an arithmetic progression. The inner rectangle is one foot wide, the first shaded region is 2 feet wide on all four sides of the inner rectangle, and the second shaded region is 3 feet wide on all four sides of the previous region. What is the length in feet of the inner rectangle?
A) 10
B) 20
C) 40
D) 50
E) 60

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