
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
Matrix and Transformation: Given $a, b \in \mathbb{R}$, if the matrix $$M= \begin{bmatrix} -1 & a \\ b & 3\end{bmatrix}$$ corresponds to a transformation that maps the line $l: 2x-y=3$ onto itself, find $M^{-1}$.

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