
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
Consider a 3x3 grid where the distance between adjacent points is 1 unit. Two triangles are drawn on this grid such that they overlap. The first triangle connects the points at the top left, middle right, and bottom center. The second triangle connects the points at the top right, middle left, and bottom center. What is the area of the region where these two triangles overlap?

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