
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
Let \( L_{1} \) be the line with equation \( 6x - y + 6 = 0 \). Let \( P \) and \( Q \) be the points of intersection of \( L_{1} \) with the \( x \)-axis and \( y \)-axis, respectively. A line \( L_{2} \) that passes through the point \( (1,0) \) intersects the \( y \)-axis and \( L_{1} \) at \( R \) and \( S \), respectively. If \( O \) denotes the origin and the area of \( \triangle OPQ \) is six times the area of \( \triangle QRS \), find all possible equations of the line \( L_{2} \). Express your answer in the form \( y = mx + b \).

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