
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
Elective 4-2: Matrices and Transformations  
Given a second-order matrix $M$ with an eigenvalue $\lambda=3$ and a corresponding eigenvector $\overrightarrow{e_{1}} = \begin{bmatrix} 1 \\ 1\end{bmatrix}$, and the transformation corresponding to $M$ maps the point $(-1, 2)$ to $(9, 15)$, find the matrix $M$.

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