
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
Find the equation of the curve $2x^{2}-2xy+1=0$ after it undergoes a transformation corresponding to the matrix $N=\begin{bmatrix} 1 & 0 \\ -1 & 1 \end{bmatrix}$, followed by a transformation corresponding to the matrix $M=\begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}$.

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