
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 large rectangular room measures $a$ by $b$ feet, where $a$ and $b$ are positive integers with $b > a$. If a decorator decides to place carpet leaving a uniform unpainted border of width 2 feet all around, and the unpainted area occupies one-third of the area of the entire floor, how many possible ordered pairs $(a, b)$ fit these criteria?
**A)** 1
**B)** 2
**C)** 3
**D)** 4
**E)** 5

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