
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 $((m^{2}-2m-3)x+(2m^{2}+m-1)y+6-2m=0)$ where $m\in R$.
(1) Find the condition for which the equation represents a line;
(2) Find the value of $m$ for which the slope of the line does not exist. Derive the equation of the line in this case;
(3) Given that the $x$-intercept of the line $l$ represented by the equation is $-3$, find the value of $m$;
(4) If the line $l$ represented by the equation has an angle of inclination of $45^{\circ}$, find the value of $m$.

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