
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 equations for lines $l_1$ and $l_2$ respectively: $l_1: 2x + y + 4 = 0$, $l_2: ax + 4y + 1 = 0$.  
(1) When $l_1 \perp l_2$, find the coordinates of the intersection of $l_1$ and $l_2$.  
(2) When $l_1 \parallel l_2$, calculate the distance between $l_1$ and $l_2$.

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