
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 rectangular floor measures a by b feet, where a and b are positive integers and b > a. The unpainted part of the floor forms a border of width 2 feet around the painted rectangle and occupies one third of the area of the whole floor. Calculate the number of possibilities for the ordered pair (a, b).

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