
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 complex number $z = (m-1)(m+2) + (m-1)i$ where $m$ is a real number and $i$ is the imaginary unit,
1. If $z$ is a pure imaginary number, find the value of $m$.
2. If the point corresponding to the complex number $z$ in the complex plane is located in the fourth quadrant, determine the range of value for the real number $m$.
3. If $m = 2$, and $\frac {z+i}{z-1}$ can be expressed as $a+bi$ (where $a$, $b\in\mathbb{R}$), find the value of $a+b$.

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