
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 $l: x-2y+1=0$.  
$(1)$ If the line $l_{1}: 2x+y+1=0$, find the angle between the lines $l$ and $l_{1}$.  
$(2)$ If the distance between the line $l_{2}$ and $l$ is $1$, find the general equation of the line $l_{2}$.

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