
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 $x$, $y \in \mathbb{R}$, the vector $\overrightarrow{a}= \begin{bmatrix} 1 \\ 1\end{bmatrix}$ makes the second-order matrix $A= \begin{bmatrix} a & 2 \\ b & 4\end{bmatrix}$ have an eigenvector corresponding to the eigenvalue $3$. Find the equation of the line $l'$, which is the transformation of the line $l: 2x-y-3=0$ under the matrix $A$.

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