
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 = $$\begin{bmatrix} 1 & 0 \\ 0 & 2\end{bmatrix}$$, B = $$\begin{bmatrix} 1 & 2 \\ 0 & 1\end{bmatrix}$$, if line $l$ undergoes transformations $T\_A$, $T\_B$ in sequence to obtain line $l'$: 2x + y - 2 = 0, find the equation of line $l$.

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