
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 slope of line $l_{1}$ is $2$, line $l_{2}$ passes through point $A\left(3m,2m-1\right)$ and $B\left(2,m-3\right)$.  
$(1)$ If the inclination angle of line $l_{2}$ is $45^{\circ}$, find the value of $m$;  
$(2)$ If $l_{1}\bot l_{2}$, find the value of $m$.

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