
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
A 3x3 grid of points is spaced equally both horizontally and vertically, with each adjacent point 1 unit apart. Two triangles are drawn on this grid: the first triangle connects the top-left corner, middle of the right edge, and bottom-center point; the second triangle connects the bottom-left corner, middle of the top edge, and right-center point. Calculate the area in square units where these two triangles overlap.

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