
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 $$M= \begin{bmatrix} 1 & 2 \\ a & 1\end{bmatrix}$$ with one of its eigenvalues being λ=3, and its corresponding eigenvector being $$\overrightarrow {α}= \begin{bmatrix} \overset{1}{1}\end{bmatrix}$$, find the equation of the curve l<sub>2</sub> resulting from the transformation of the line l<sub>1</sub>: x+2y+1=0 under matrix M.

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