
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 garden measures $c$ by $d$ feet, where $c$ and $d$ are positive integers, and $d > c$. A gardener decides to plant flowers in a rectangular section of the garden with the sides of the section parallel to the garden edges. The unplanted part of the garden forms a border of width $2$ feet around the flower section and occupies one-third the area of the whole garden. Find the number of possibilities for the ordered pair (c,d).

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