
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 $$A= \begin{bmatrix} a & b \\ c & d\end{bmatrix}$$, if matrix A has an eigenvector $$\overrightarrow {α_{1}}$$ corresponding to the eigenvalue 6 as $$\begin{bmatrix} 1 \\ 1\end{bmatrix}$$, and an eigenvector $$\overrightarrow {α_{2}}$$ corresponding to the eigenvalue 1 as $$\begin{bmatrix} 3 \\ -2\end{bmatrix}$$, find the inverse matrix of A.

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