
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 nine points of this grid are equally spaced horizontally and vertically. The distance between two neighboring points is 1 unit. Suppose the first triangle is formed by connecting the points at coordinates (0,0), (2,2), and (2,0) and the second triangle is formed by connecting the points at (0,2), (2,2), and (0,0). What is the area, in square units, of the region where the two triangles overlap?

[asy]
size(80);
dot((0,0)); dot((0,1));dot((0,2));dot((1,0));dot((1,1));dot((1,2));dot((2,0));dot((2,1));dot((2,2));
draw((0,0)--(2,2)--(2,0)--cycle, linewidth(0.6));
draw((0,2)--(2,2)--(0,0)--cycle, linewidth(0.6));
[/asy]

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