
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
In the Cartesian coordinate system $xOy$, the point $(2, -2)$ is transformed by the matrix $M=\begin{pmatrix}0 & 1 \\ a & 0\end{pmatrix}$ to the point $(-2, 4)$. The curve $C: x^2+y^2=1$ is transformed by the matrix $M$ to the curve $C'$. Find the equation of the curve $C'$.

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