
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 $A$, the matrix $A$ has an eigenvector $\alpha_1 = \begin{pmatrix}1\\0\end{pmatrix}$ corresponding to the eigenvalue $\lambda_1 = -1$, and another eigenvector $\alpha_2 = \begin{pmatrix}0\\1\end{pmatrix}$ corresponding to the eigenvalue $\lambda_2 = 4$. Find the matrix $A$.

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