
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 garden measuring $a$ by $b$ meters, with $a$ and $b$ being positive integers where $b > a$, an area is set aside for planting, which is a rectangle with sides parallel to the sides of the garden, and a path of width $2$ meters surrounds the planting area within the garden and covers one-third of the total area of the garden. Determine the number of possibilities for the ordered pair $(a, b)$.

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