
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 that two lines l<sub>1</sub>: 3x + 4y - 2 = 0 and l<sub>2</sub>: 2x + y + 2 = 0 intersect at point P.

1. Find the equation of the line passing through point P and the origin.
2. Find the equation of the line l passing through point P and perpendicular to line l<sub>3</sub>: 2x + y + 2 = 0.

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