
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 equation of the line $l$ as $2x+y+1=0$.  
$(1)$ Find the equation of the line $l_{1}$ passing through point $A(3,2)$ and perpendicular to line $l$.  
$(2)$ Find the equation of line $l_{2}$ that satisfies the following conditions:  
① Parallel to line $l$;  
② The distance from point $P(3,0)$ to line $l_{2}$ is $\sqrt{5}$.

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