
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
Let $M$ be the transformation that stretches the x-coordinate by 2 times and the y-coordinate by 3 times on the coordinate plane.  
(Ⅰ) Find the eigenvalues and the corresponding eigenvectors of matrix $M$;  
(Ⅱ) Find the inverse matrix $M^{-1}$ and the equation of the new curve formed by the ellipse $\frac {x^{2}}{4}+ \frac {y^{2}}{9}=1$ under the transformation of $M^{-1}$.

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