
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
Given the curve $C$: $(x-y)^{2}+y^{2}=1$ is transformed by the matrix $A \begin{bmatrix} 2 & -2 \\ 0 & 1\end{bmatrix}$ to obtain the curve $C'$, then the equation of the curve $C'$ is \_\_\_\_\_\_.

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