
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
1. Given that the angle of inclination of line $l$ is half of that of line $m: y = -\sqrt{3}x + 1$, find the equation of the line that passes through point $P(2, 2)$ and is perpendicular to line $l$.
2. Given that line $l$ passes through point $Q(3, -2)$ and has equal intercepts on the two coordinate axes, find the equation of $l$.

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