
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 measuring $a$ by $b$ feet, where $a$ and $b$ are positive integers and $b > a$, an artist paints a rectangle on the floor with the sides of the rectangle parallel to the floor. The unpainted part of the floor forms a border of width $2$ feet around the painted rectangle and occupies half the area of the whole floor. Determine the number of possibilities for the ordered pair $(a,b)$.

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