
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
In the Cartesian coordinate plane $(xOy)$, the line $x + y - 2 = 0$ is transformed into the line $x + y - b = 0 (a, b \in \mathbb{R})$ under the transformation corresponding to the matrix $A = \begin{bmatrix} 1 & a \\ 1 & 2 \end{bmatrix}$. Find the value of $a + b$.

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