
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

Construct the image of the square with vertices \( A(0,0), B(0,2), C(2,2), D(2,0) \) under the following transformations:
a) \( w = i z \)
b) \( w = 2 i z - 1 \)
c) \( w = z^{2} \)
d) \( w = z^{-1} \)

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