
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 that the equation of line $l_{1}$ is $2x+y-4=0$, if line $l_{2}$ passes through the point $(-3,0)$ and is perpendicular to $l_{1}$.  
$(1)$ Find the equation of line $l_{2}$.  
$(2)$ Given that line $m$ passes through the intersection point of lines $l_{1}$ and $l_{2}$ and has equal intercepts on the two coordinate axes, find the equation of line $m$.

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