
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 $a, b \in \mathbb{R}$, vector $\overrightarrow {a} = \begin{bmatrix} b \\ 1 \end{bmatrix}$ is an eigenvector of matrix A = $\begin{bmatrix} a & 2 \\ 2 & -3\end{bmatrix}$ corresponding to the eigenvalue -4, find matrix A and its other eigenvalue.

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