
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 matrices M= $$\begin{bmatrix} 0 & -1 \\ 1 & 0\end{bmatrix}$$ and N= $$\begin{bmatrix} 2 & 1 \\ -1 & -2\end{bmatrix}$$:

1. Find the product MN.
2. If curve C₁: x²-y²=1 is transformed under the corresponding action of matrix MN to obtain another curve C₂, find the equation of C₂.

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