
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 $m \in \mathbb{R}$, the complex number $z= \frac {m-2}{m-1}+(m^{2}+2m-3)i$, for what value(s) of $m$ does:  
(1) $z$ belong to $\mathbb{R}$;  
(2) $z$ is a pure imaginary number;  
(3) the point corresponding to $z$ is located in the second quadrant of the complex plane.

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