
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 second-order matrix $A= \begin{bmatrix} 3 & 5 \\ 0 & -2\end{bmatrix}$.
(1) Find the eigenvalues and eigenvectors of matrix A;
(2) Suppose vector $\overrightarrow{\beta} = \begin{bmatrix} 1 \\ -1\end{bmatrix}$, calculate $A^{2016} \overrightarrow{\beta}$.

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