
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 $m$, $n$ $\in\mathbb{R}$, vector $\overrightarrow {a}$\= $\begin{bmatrix} \overset{1}{1}\end{bmatrix}$ is a characteristic vector of matrix $M= \begin{bmatrix} \overset{1     m}{2     n}\end{bmatrix}$ corresponding to the eigenvalue 3, find matrix $M$ and its other eigenvalue.

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