
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 $a, b \in \mathbb{R}$, if point $M(1, 2)$ is transformed to point $N(2, -7)$ under the transformation corresponding to matrix $A= \begin{bmatrix} a & 1 \\ b & 4\end{bmatrix}$, find the eigenvalues of matrix $A$.

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