
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 $l_1: 2x-y-3=0$ and $l_2: x-my+1-3m=0$, where $m\in \mathbb{R}$.
$(1)$ If $l_1\parallel l_2$, find the value of the real number $m$;
$(2)$ If $l_2$ has equal intercepts on both coordinate axes, find the equation of the line $l_2$.

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