
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 two lines $l_1: x - 2y + 3 = 0$ and $l_2: 2x + 3y - 8 = 0$, their intersection point is $M$,

(1) Find the equation of line $l$ that passes through point $M$ and is at a distance of 2 from point $P(0, 4)$;  
(2) Find the equation of line $l$ that passes through point $M$ and is parallel to line $l_3: x + 3y + 1 = 0$.

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