
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 a rectangular floor that measures $a$ by $b$ feet, where $a$ and $b$ are positive integers with $b > a$, the area of the unpainted part is equal to one-third the area of the entire floor. The unpainted part forms a border of width $2$ feet around the painted rectangle, and the sides of the rectangle are parallel to the sides of the floor.

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