
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 field measures $a$ by $b$ meters, where $a$ and $b$ are positive integers and $b > a$. To create a play area, a field manager decides to mark a smaller rectangle within the field, aligned with the field’s borders. Around this smaller rectangle, a uniform walking path 2 meters wide covers one third of the total area. Determine the number of possible $(a, b)$ pairs that meet these conditions.

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