
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 $A= \begin{bmatrix} 1 & 2 \\ -2 & -3 \end{bmatrix}$ and $B= \begin{bmatrix} 0 & 1 \\ 1 & -2 \end{bmatrix}$.

(Ⅰ) Find the inverse of matrix $A$, $A^{-1}$, and the matrix $X$ that satisfies $AX=B$.

(Ⅱ) Find the equation of curve $C'$ that is the result of applying the linear transformation associated with matrix $B$ to the curve $C$ with equation $x^2 - 4xy + y^2 = 1$.

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