
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  $n$  be an integer greater than  $3$ . A square of side length  $n$  is divided by lines parallel to each side into  $n^2$  squares of length  $1$ . Find the number of convex trapezoids which have vertices among the vertices of the  $n^2$  squares of side length  $1$ , have side lengths less than or equal  $3$  and have area equal to  $2$ Note: Parallelograms are trapezoids.

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