
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 $i$ as the imaginary unit, let complex numbers $z_{1}=1+i$ and $z_{2}=m-2i\left(m\in R\right)$.  
$(1)$ If $z_{1}+z_{2}=2-i$, find the value of the real number $m$.  
$(2)$ If the point corresponding to $z_{1}\cdot z_{2}$ on the complex plane is located in the right half-plane (excluding the imaginary axis), find the range of values for the real number $m$.

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