
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 $(m^{2}-2m-3)x+(2m^{2}+m-1)y+5-2m=0$ ($m\in\mathbb{R}$).

(1) Find the condition for which the equation represents a line;

(2) Find the value of $m$ when the line represented by the equation is perpendicular to the $x$-axis;

(3) Find the real value of $m$ if the line represented by the equation has equal intercepts on both coordinate axes.

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