
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 $l_1: 2x + 4y - 1 = 0$, and line $l_2$ passing through the point $(1, -2)$, find the equation of line $l_2$ that satisfies the following conditions:
(1) $l_1 \parallel l_2$;
(2) $l_1 \perp l_2$.

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