
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 grid where points are spaced 1 unit apart both horizontally and vertically. There are ten points on this grid. Two triangles are formed with vertices at these points. One triangle has vertices at coordinates (0,0), (3,0), and (1,2). The other triangle has vertices at coordinates (3,2), (0,1), and (1,0). Calculate the area, in square units, of the region where these two triangles overlap.

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