
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 $M= \begin{bmatrix} 1 & b \\ c & 2 \end{bmatrix}$ has an eigenvalue $\lambda_1 = 4$ and a corresponding eigenvector $\overrightarrow{e_1}= \begin{bmatrix} 2 \\ 3 \end{bmatrix}$.
1. Find the matrix $M$;
2. Find the equation of the new curve after transforming the curve defined by $5x^2 + 8xy + 4y^2 = 1$ under the action of matrix $M$.

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