
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 the matrix $$A= \begin{bmatrix} \left.\begin{matrix}3 & 0 \\ 0 & 4\end{matrix}\right.\end{bmatrix}$$, and points M(-1, -1), N(1, 1).
(1) Find the length of the line segment M'N' obtained after the transformation by matrix A on the line segment MN;
(2) Find the eigenvalues and eigenvectors of matrix A.

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