
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 the intersection point $P$ of two lines $l_{1}$: $x+y-2=0$ and $l_{2}$: $2x+y+2=0$, find the equation(s) of the line(s) that satisfy the following conditions:
1. Passes through point $P$ and the origin.
2. Passes through point $P$ and is perpendicular to line $l_{3}$: $x-3y-1=0$.

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