
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
In a 3x3 grid where the points are equally spaced both horizontally and vertically by 1 unit each, two triangles are formed with the following vertices: The first triangle has vertices at the top-left corner, middle-right edge, and bottom-left corner of the grid. The second triangle has vertices at the top-right corner, middle-left edge, and bottom-right corner of the grid. Calculate the area, in square units, of the region where the two triangles intersect.

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