
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 grid with points spaced horizontally and vertically 1 unit apart is provided. Consider a square and a triangle drawn on this grid, where the square has side length 2 units and the triangle is isosceles with a base and height of 2 units. The square has vertices at (0,0), (2,0), (2,2), and (0,2). The triangle has vertices at (3,0), (1,2), and (2,1). What is the area, in square units, of the region where the square and the triangle overlap?

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