
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 the rectangle \(ABCD\) with an area of 1 square unit. Let \(O\) be the center of the incircle of the triangle formed by the vertices \(A, B,\) and \(C\). Now consider a rectangle with vertices \(O\) and \(D\) as opposite corners, and the other two vertices lying on the perimeter of the original rectangle. What is the area of this new rectangle?

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