
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]


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Elective 4-2: Matrix and Transformation

Let $a, b \in \mathbb{R}$. If the line $l: ax+y-7=0$ is transformed under the action of matrix $A=\begin{bmatrix} 3 & 0 \\ -1 & b \end{bmatrix}$ to line $l': 9x+y-91=0$, find the values of the real numbers $a$ and $b$.

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