
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
On a 3x3 grid, where the distance between adjacent points is 1 unit, place the first right triangle by connecting points (0,0), (2,2), and (0,2). Place the second triangle, also right-angled, by connecting points (2,0), (0,2), and (2,2). What is the area, in square units, of the region where these two triangles overlap?

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