
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 the line $l: 2x-y=3$, if the matrix $A= \begin{pmatrix} -1 & a \\ b & 3 \end{pmatrix}$ with $a, b \in \mathbb{R}$ corresponds to the transformation $\sigma$ that maps line $l$ onto itself.  
(Ⅰ) Find the matrix $A$;  
(Ⅱ) Find the inverse matrix of $A$.

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