
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 line $y=-\frac{\sqrt{3}}{3}x+5$, the angle of inclination of this line is five times the angle of inclination of the sought line $l$. The line $l$ satisfies the following conditions (express the result in the general form):
(1) If it passes through point P(3, -4), find the equation of line $l$.
(2) If it has an x-intercept of -2, find the equation of line $l$.
(3) If it has a y-intercept of 3, find the equation of line $l$.

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