
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
For the complex numbers $z\_1=m+i$ and $z\_2=m+(m-2)i$, where $i$ is the imaginary unit and $m$ is a real number:

1. Find the range of $m$ if the point corresponding to $z\_2$ in the complex plane lies in the fourth quadrant.
2. Find the values of the real numbers $m$ and $n$ if $z\_1$ and $z\_2$ satisfy the equation $z\_2=z\_1 \cdot ni$.

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