
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
Let \( OABC \) be a rectangle in the \( xy \)-plane with vertices \( O(0,0), A(2,0), B(2,3), C(0,3) \). Consider a transformation defined by \( u = x^2 - y^2 + 1 \) and \( v = xy \). Find the image of rectangle \( OABC \) in the \( uv \)-plane.

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