
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
Let  $n>3$  be a positive integer. Equilateral triangle ABC is divided into  $n^2$  smaller congruent equilateral triangles (with sides parallel to its sides). Let  $m$  be the number of rhombuses that contain two small equilateral triangles and  $d$  the number of rhombuses that contain eight small equilateral triangles. Find the difference  $m-d$  in terms of  $n$ .

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