
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 that $$\begin{pmatrix} k \\ 0 \end{pmatrix}$$ is an eigenvector of the matrix $A= \begin{pmatrix} 1 & 0 \\ m & 2 \end{pmatrix}$.

(Ⅰ) Find the value of $m$ and the corresponding eigenvalue for the vector $$\begin{pmatrix} k \\ 0 \end{pmatrix}$$;

(Ⅱ) If the matrix $B= \begin{pmatrix} 3 & 2 \\ 2 & 1 \end{pmatrix}$, find the matrix $B^{-1}A$.

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