
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 matrix M $$\begin{pmatrix} \left.\begin{matrix}2 & -3 \\ 1 & -1\end{matrix}\right.\end{pmatrix}$$ corresponds to a linear transformation that transforms point A $(x, y)$ into point A′ $(13, 5)$. Try to find the inverse matrix of M and the coordinates of point A.

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