
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 $a$, $b∈R$, matrix $A= \begin{bmatrix} \left.\begin{matrix}-1 & a \\ b & 3\end{matrix}\right.\end{bmatrix}$ corresponds to a transformation $T_{A}$ that transforms the line $2x-y-3=0$ into itself. Find the values of real numbers $a$ and $b$.

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