
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 square $OABC$ in the $xy$-plane with vertices $O(0,0), A(2,0), B(2,2),$ and $C(0,2)$. Define transformations $u=x^3-y^3$ and $v=x^2y^2$. What is the image of the larger square $OABC$ in the $uv$-plane?
A) [(0,0), (9,0), (0,90), (-9,0)]
B) [(0,0), (8,0), (0,16), (-8,0)]
C) [(1,0), (8,0), (1,16), (-8,1)]
D) [(0,1), (8,5), (0,15), (-7,0)]

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