
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 $A= \begin{bmatrix} 3 & 3 \\ 2 & 4 \end{bmatrix}$.
1. Find the inverse matrix $A^{-1}$ of matrix $A$;
2. Find the eigenvalues and eigenvectors of matrix $A$;
3. Find the equation of the curve obtained after the transformation corresponding to matrix $A$ is applied to the circle $x^2+y^2=1$.

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