
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 the equation to represent a line;
(2) For what value of $m$ does the equation represent a line perpendicular to the x-axis;
(3) If the line represented by the equation has equal intercepts on both coordinate axes, find the value of the real number $m$.

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