
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
Suppose there is a grid with points equally spaced horizontally and vertically, with a distance of 2 units between neighboring points. Determine the area, in square units, where the following two triangles overlap: one triangle is defined by the vertices at (0,0), (4,2), and (2,4), and another triangle with vertices at (4,4), (0,2), and (2,0).

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