
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 a complex number $z=bi(b\in\mathbb{R})$, $\frac{z-2}{1+i}$ is a real number, where $i$ is the imaginary unit.
1. Find the complex number $z$.
2. If the point represented by the complex number $(m+z)^{2}$ is in the first quadrant, find the range of the real number $m$.

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