
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
[Optional Question] Given that the second-order matrix M belongs to the eigenvalue 3 and one of its eigenvectors is $$\overrightarrow {e}= \begin{bmatrix} \overset{1}{1}\end{bmatrix}$$, and the transformation corresponding to matrix M turns the point (-1, 2) into the point (9, 15), find the matrix M.

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