
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
The diagram below shows two parallel rows with seven points in the upper row and nine points in the lower row. The points in each row are spaced one unit apart, and the two rows are two units apart. How many trapezoids which are not parallelograms have vertices in this set of  $16$  points and have area of at least six square units?
[asy]
import graph; size(7cm); 
pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps);
pen dotstyle = black;
dot((-2,4),linewidth(6pt) + dotstyle); 
dot((-1,4),linewidth(6pt) + dotstyle); 
dot((0,4),linewidth(6pt) + dotstyle); 
dot((1,4),linewidth(6pt) + dotstyle); 
dot((2,4),linewidth(6pt) + dotstyle); 
dot((3,4),linewidth(6pt) + dotstyle); 
dot((4,4),linewidth(6pt) + dotstyle); 
dot((-3,2),linewidth(6pt) + dotstyle); 
dot((-2,2),linewidth(6pt) + dotstyle); 
dot((-1,2),linewidth(6pt) + dotstyle); 
dot((0,2),linewidth(6pt) + dotstyle); 
dot((1,2),linewidth(6pt) + dotstyle); 
dot((2,2),linewidth(6pt) + dotstyle); 
dot((3,2),linewidth(6pt) + dotstyle); 
dot((4,2),linewidth(6pt) + dotstyle); 
dot((5,2),linewidth(6pt) + dotstyle); [/asy]

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