
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 each point is spaced 1 unit apart both horizontally and vertically. A rectangle is defined by the points (0,0), (3,0), (3,2), and (0,2). A right triangle with vertices at (2,0), (2,2), and (4,2) overlaps partially with the rectangle. What is the area, in square units, of the region where the rectangle and the triangle overlap?

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