
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 grid has nine equally spaced points forming a 3x3 grid with a distance of 1 unit between each neighboring point. What is the area, in square units, of the region where a triangle with vertices at the top left, middle right, and bottom left of the grid overlaps with another triangle having vertices at the top right, middle left, and bottom right?

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