
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 transformation T that maps points $(1,\frac{1}{2}),(0,1)$ in the plane to points $(\frac{9}{4},-2),(-\frac{3}{2},4)$ respectively. Let the matrix associated with the transformation T be M.
(1) Find the matrix M;
(2) Determine the eigenvalues of the matrix M.

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