
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 matrices $$A= \begin{bmatrix} \left.\begin{matrix}1 & 0 \\ 0 & 2\end{matrix}\right.\end{bmatrix}$$ and $$B= \begin{bmatrix} \left.\begin{matrix}1 & \frac {1}{2} \\ 0 & 1\end{matrix}\right.\end{bmatrix}$$, if the transformation corresponding to matrix AB turns line $l: x+y-2=0$ into line $l'$, find the equation of line $l'$.

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