
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 room measures $p \times q$ feet where $p$ and $q$ are positive integers with $q > p$. An interior designer wishes to lay carpet in the room such that a uniform bare border of 2 feet is left around the carpeted area. This bare border occupies one-third of the area of the entire room. Determine how many possibilities exist for the pair $(p, q)$.

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