
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 $m$ by $n$ feet, where $m$ and $n$ are positive integers with $n > m$, the unpainted part of the floor, a border around the painted area, is $2$ feet wide on each side and occupies one-third of the area of the entire floor. Determine how many possibilities there are for the ordered pair $(m,n)$.

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