
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 $T$ which maps points $(1, \frac {1}{2})$ and $(0,1)$ on the plane to the points $( \frac {9}{4},-2)$ and $(- \frac {3}{2},4)$, respectively. Let the matrix corresponding to the transformation $T$ be $M$.  
(1) Find the matrix $M$;  
(2) Find the eigenvalues of the matrix $M$.

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