
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 $A=\left[\begin{matrix}2 & 0 \\ -1 & 1\end{matrix}\right]$ and $B=\left[\begin{matrix}2 & 4 \\ 3 & 5\end{matrix}\right]$, and the second-order matrix $M$ satisfies $AM=B$.
(1) Find $A^{-1}$;
(2) Find the matrix $M$.

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