
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 the lines $2x - y - 4 = 0$ and $x - 2y + 1 = 0$ intersect at point $P$.
(1) Find the equation of line $l\_1$ that passes through point $P$ and is perpendicular to the line $3x + 4y - 15 = 0$. (Express the result in the general form of a linear equation)
(2) Find the equation of line $l\_2$ that passes through point $P$ and has equal intercepts on both coordinate axes. (Express the result in the general form of a linear equation)

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