
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 $A= \begin{pmatrix} 1 & 1 \\ 2 & 3\end{pmatrix}$, $B= \begin{pmatrix} 1 & 2 \\ 2 & 3\end{pmatrix}$.  
(I) Find the inverse matrix $A^{-1}$ of matrix A;  
(II) Find the equation of the curve obtained by the linear transformation corresponding to $A^{-1}B$ acting on the line $x+y-1=0$.

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